
Review Article


Regulated OFDMRole of ECC and ANN: A Review 

Padmapriya Praveenkumar,
Rengarajan Amirtharajan,
K. Thenmozhi
and
John Bosco Balaguru Rayappan



ABSTRACT

Orthogonal Frequency Division Multiplexing (OFDM) has come to the rescue of the bandwidth constraint owing to the burgeoning digital multimedia applications. The serial data is made parallel and transmitted over multiple orthogonal frequencies with bandwidth of each subcarrier considerably lesser than the coherence bandwidth of the channel. This study aims to review the present state of art in Error Correcting Codes (ECC) in OFDM, generated by methods like Convolutional Encoding, using ReedSolomon Codes and Turbo codes. Furthermore the deployment of Artificial Neural Networks (ANN), to train the system for higher fault tolerance in OFDM is detailed.





Received: December 18, 2011;
Accepted: January 24, 2012;
Published: March 21, 2012


INTRODUCTION
In Today’s multimedia communication scenario, a growing demand emerges
for highspeed, reliable, highquality digital data. These trends place significant
challenges to the parallel data transmission scheme which alleviates the problems
encountered with serial systems. High spectral efficiency and resilience to
interference caused by multipath effects are the fundamentals to meet the requirements
of today’s wireless communication. The onset of Orthogonal Frequency Division
Multiplexing (OFDM) has raised the wireless standards to 50 Mbps and higher,
which creates a revolutionary in the wireless business. The first multichannel
modulation systems transmitting binary data transmission over the SSB voice
channel were implemented by Doelz et al. (1957).
Multicarrier Modulation scheme was invented by Chang (1970)
who proposed the orthogonality concept. Holsinger, (1964)
determined the performance of fixed time continuous channel with memory and
Intersymbol interference. Saltzberg (1967) describes
the effective parallel transmission, combating the effects of amplitude and
delay distortion.
Zimmerman and Kirsch (1967) introduces the effective
utilization of the spectrum with high data rate. Chang and
Gibby (1968) presents a theoretical analysis on the performance of orthogonally
multiplexed data transmission. FDM made more practical through DFT was proposed
by Weinstein and Ebert (1971). The concept of frequencydomain
data transmission by IDFT and DFT was described by Peled
and Ruiz (1980). Cimini (1985) introduced OFDM in
the wireless market place. Mathematical analysis of multipath radio propagation
channel was described by Chung (1987). Bingham
(1990) illustrates that Multicarrier Modulation (MCM) provides greater immunity
towards noise and fades. Highspeed wireless connectivity to the users accommodating
COFDM in TDAB and DFT based DMT have become the standard for ADSL (Akansu
et al., 1998). Furthermore suitability of COFDM in telemedicine applications
and multimedia data transmission is available in study of Thenmozhi
and Prithiviraj (2008). The Space Time Frequency coded (STF) OFDM for broadband
wireless communication systems is available in study of (Thenmozhi
et al., 2011).
The increase in the symbol duration of OFDM Symbol for lower rate parallel
streams and the relative decrease in the amount of dispersion in time caused
by multipath delay spread has been explained in Bahai et
al. (2004). Sending confidential information without affecting the regular
OFDM operation is available in studies of Balaguru et
al. (2010), Kumar et al. (2011) and Thenmozhi
et al. (2011).
This study has taken a maiden effort to present a concise explanation on OFDM,
A detailed description on Error Correcting Codesnamely, Convolutional Codes
(CC), ReedSolomon (RS) Codes and Turbo codes along with Artificial Neural Network
(ANN) deployment in OFDM. To start with, an introduction to the OFDM system
has been explained by Thenmozhi (2008). Followed by an
OFDM performance and the associated problems are enumerated. Later, Various
Error control codes are discussed. Penultimate Section addresses, how OFDM problems
are coped with error control codes and neural networks. Finally, the concluding
remarks are discussed in detail.
OFDM SYSTEM DESCRIPTION
OFDM is a parallel transmission scheme where serial baseband high rate data
bits are split into slow rate parallel data bits is shown in the Fig.
1. Willink and Wittke (1997) proposed that multicarrier
transmission provides significant improvement in channel SNR. Since multiple
carriers are used for transmission, the frequency selectivity of the wideband
channel experienced by singlecarrier transmission is overcome Casas
and Leung (1991). The parallel data stream is modulated on different subcarriers
making the subcarriers bandwidth very small when compared with the channel’s
coherence bandwidth. The symbol period of the sub streams is made long compared
to the delay spread of the channel.
They are then passed on to a signal mapper to produce N constellation data
points depending on the modulation techniques used. It may be BPSK, QPSK or
QAM. Kalet (1989) investigated multipath QAM provides
better results than sigletone QAM. N is taken as an integer raised to the power
of two, enabling the highly efficient FFT algorithms for modulation and demodulation.
Then IFFT is used for modulating these data points on a set of orthogonal subcarriers
(Arioua et al., 2012). N symbol is extended to
NTs due to Serial to Parallel (SP) conversion, so the length of the OFDM symbol
T_{sym} = NTs.
Let the lth OFDM signal at kth subcarrier be denoted as ι_{l,k(t)}: Discrete time OFDM symbol can be expressed as: Received OFDM symbol is: X_{l}(k ), the transmitted symbol can be reconstructed using orthogonality principle. The subcarriers can be represented as complex exponential signals:
at f_{k} = k/T_{sym} in OFDM signal where 0≤t≤T_{sym}.

Fig. 1: 
OFDM system model 
The subcarriers are said to be orthogonal if their integral product for their common period is zero:
The output data will be in time domain. Guard Interval (GI) is introduced to
preserve the orthogonality of the subcarriers (SCs) and is independent of subsequent
OFDM symbols. The cyclic prefix which is transmitted during GI, copied the last
part of OFDM symbol and pasted into the guard interval whose length should always
exceed the maximum delay of the multipath channel as shown in Fig.
2. Elahmar et al. (2007) introduced a new
algorithm in OFDM system called MERRY (Multicarrier Equalization by Restoration
of Redundancy) which blindly and adaptively shorten the length of the channel
to that of GI. The transmitted signal becomes periodic and the effect of the
timedispersive multipath channel becomes equivalent to a cyclic convolution,
discarding the GI at the receiver. The GI is selected to have a length of one
tenth to a quarter of the symbol period, leading to an SNR loss of 0.5 to 1
dB.
Orthogonality among six sinusoidal signals was taken which generated a matrix of signal vectors X_{i} in each row. To check the orthogonality, product of X_{i} and the transpose of X_{i} are taken and the results are shown in Fig. 3.
Complexity comparison between DFT and FFT computed by Hirosaki
(1981) is summarized in Table 1.
Baseband OFDM can be expressed as:
Multicarrier modulation at the transmitter and receiver can be implemented
by using IFFT and FFT respectively and a sample for N = 3 is shown in Fig.
4 and the time domain representation is given in Fig. 5.

Fig. 2: 
OFDM symbol with cyclic prefix (CP) 

Fig. 3: 
Orthogonality among subcarriers 

Fig. 4: 
Modulation and demodulation of OFDM with N = 3 
Table 1: 
Summarized froms of the number of multiplications per output
sample 

M: Order of the highrate FIR filter G(z), L: Number of sub
bands, N: Baseband Data channels, A: The fractional part of f1/f0, f1: Frequency
of the first channel, f0: Baud rate 1/T 
Table 2: 
Parameters of OFDM 

The symbol demapper detects the data by an element wise multiplication of the
FFT output by the inverse of the estimated channel frequency.
In the design of any OFDM receiver for physical layer IEEE802.11a (Thenmozhi
et al., 2006), time and frequency synchronization are paramount to
identify the start of the OFDM symbol and to align the local oscillator frequencies
at the transmitter and receiver end . If there is any inaccuracy in any of the
synchronization tasks, the orthogonality of the SCs is lost and this results
in Intersymbol Interference (ISI) and Inter Carrier Interference (ICI). Jiang
et al. (2010) simulated the joint proposal of Adaptive soft Frequency
Reuse (AFR) and Maximum Ratio Combining (MRC) which mitigates ICI significantly.
Out of the 52 OFDM subcarriers, 4 are pilot subcarriers and remaining are for carrying Data with a carrier separation of 20/64 MHz = 0.3125 MHz. The subcarriers can be from BPSK, QPSK or QAM. The occupied bandwidth is around 16.6 MHz from the total 20 MHz Bandwidth which is given in Table 2. The symbol duration is 4 μsec including a guard interval of 0.8 μsec. GI in OFDM symbols eliminates ISI caused by multipath propagation. It also eliminates the need of pulseshaping filter and reduces time synchronization problems. When transmitted through Digital to analog converter, a high peak power signal is generated.
Windowing is a technique used to reduce side lobes of the received rectangular
pulses thereby reducing the out of band transmitted signal. In OFDM, windowing
must not influence the signal during its effective period. Kumar
et al. (2008) have introduced time domain windowing scheme which
considerably reduces ICI in comparison with the frequency domain techniques.
Cyclic prefix and extended GI enhances the robustness of the delay spread. The
orthogonality is preserved by implementing FFT at the receiver by gathering
the knowledge about the OFDM symbol period and by knowing the start time of
FFT. OFDM symbol is applied to the FFT to retrieve the data at the receiver.
Channel estimation is required to retrieve the data contained in the signal
constellation points. Liu et al. (2006) proposed
a new algorithm called Quasi Newton Acceleration (QNA) EM algorithm to perform
channel estimation which reduces the complexity and the number of iterations,
which enhances the BER. The receiver must have the phase reference to detect
the data. Differential detection can also be used, which compares the phases
of the symbol over adjacent subcarriers. OFDM best suits harsh multipath environments.
To maintain synchronization, OFDM includes several subcarriers as pilot carriers
that are used as phase reference for the synchronization of the receiver while
demodulating data.
Frequency interleaving ensures the fading of the bit errors resulting from the subcarriers when part of the channel bandwidth. The faded subcarriers spread out rather than being concentrated. When travelling at high speed, time interleaving mitigates severe fading. Interleaving is used to distribute the errors randomly in the bitstream. Pros:
• 
Mitigates multipath 
• 
Resilience to interference 
• 
Spectrum efficiency 
Cons:
• 
High complexity and deployment costs 
• 
Guard bands reduce efficiency 
• 
Frequency offsets require accurate AFC 
• 
Synchronization is difficult 
• 
High peaktoaverage power ratio 
Wireline applications:
• 
VDSL and ADSL (very high bit rate Digital Subscriber Line
Asymmetric Digital Subscriber Line) 
• 
MOCA (Multimedia over coax networking) 
• 
PLC (Power line communications) 
Wireless applications:
• 
IEEE 802.20 Mobile Broadband Wireless Access (MBWA) 
• 
IEEE 802.15.3a Ultra Wideband (UWB) Wireless PAN 
• 
Digital Video Broadcasting(DVB) 
• 
IEEE 802.11a, g, n (WiFi) Wireless LANs 
• 
FlashOFDM cellular systems 
• 
3GPP LTE (LongTerm Evolution) 4G mobile broadband standard downlink 
• 
IEEE 802.16 WiMAX (Worldwide Interoperability for Microwave Access) 
• 
IEEE 802.20 MBWA (Mobile Wireless MAN standard) 
• 
Digital Audio Broadcasting(DAB) 
• 
High Speed OFDM Packet Access (HSOPA) 
• 
Evolved UMTS Terrestrial Radio Access (EUTRA) 
• 
IEEE 802.22 Wireless Regional Area Networks (WRAN) 
OFDM introduces three wellknown tangles:
• 
High peaktoaverage power ratio results in Nonlinear distortion
at the poweramplification stage (Rappaport et al.,
2002) 
• 
Vulnerability to synchronization errors 
• 
Sensitive to Doppler shift 
OFDM requires accurate synchronization of time and frequency between the transmitter
and the receiver. The non ideal transmission conditions like imperfect channel
estimation, symbol frame offset, carrier and sampling clock frequency offset,
timeselective fading and critical analog components are analysed and the basic
requirements for receiver synchronization are derived (Speth
et al., 1999). If synchronization error is too large, then the orthogonality
between the SCs are lost and the system SNR degrades resulting in ISI and ICI.
Inter carrier interference also results from Doppler spreads or carrier phase
jitters. OFDM consists of independently modulated subcarriers when added up
produces large peak to average power ratio (Van Nee and Prasad,
2000). Thenmozhi et al. (2011) explained
a detailed survey on OFDM, CDMA and how to combine them effectively called as
MC CDMA for secure communication. Venkatesan and Ravichandran
(2007) analysed the performance of MC CDMA systems and concluded that it’s
the best multi access technique required by the 4G systems.
An efficient PAPR algorithm tries to reduce the BER to a minimum value (Wulich,
2005). AlKebsi (2008) introduced an algorithm by
jointly combining Modulation adaptation, power control and clipping based on
SER and SNR which provides maximum PAPR reduction (Latif
and Gohar, 2008).
Doppler shift combined with Multipath results in reflections at various frequency
and phase offsets and is very hard to compensate. Highly linear amplifiers are
used for spectral spreading and distortion. Cimini et
al. (1996) introduced clustered OFDM concept where the Peak Average
Power is reduced even when subjected to non linearity’s.
ERROR CONTROL CODES
In Wireless communication, the input data are split up over parallel carriers
resulting in nulls due to Multipath effects and selective fading. This results
in few carrier bits to be received with error. These incorrect bits can be corrected
by adding few bits to the transmitted data called the Errorcorrecting Code
(ECC). The errors in degraded carriers are corrected with the information in
the ECC, which doesn’t suffer from the same deep fade as the carrier and
hence, the name Coded OFDM. Coding can be applied across several OFDM symbols
(Zou and Wu, 1995). So, errors caused by symbols with
a large degradation can be corrected by the surrounding symbols. Here, the error
probability is no longer dependent on the power of individual symbols, but rather
on the power of a number of consecutive symbols. Seddiki
et al. (2006) evaluates BCH (BoseChaudhuriHocquenghem) codes over
OFDMBPSK modulation provides significant performance concentrating on some
of the OFDM parameters.
Convolutional encoder: Convolutional encoder is a linear sequential
circuit. The remarkable feature of the convolution encoder is that its output
is a variable quantity making it very hard to crack. Input message bits are
variable quantities and the operations take place between shift registers. Thus,
the output changes to protect the information and thereby making the code hard
to predict. Elias (1958) proposed the use of Convolutional
codes for the discrete memory less channel. Then the general understanding of
convolutional codes and sequential decoding was analysed by Viterbi
(1967). The discussion and derivation of the backward version of the Viterbi
decoding algorithm was carried out by Omura (1969).
Forney (1970) structured various algebraic theorems
on Convolutional codes. Furthermore the same author, Forney
(1971) has constructed simple asymptotically optimum codes for bursty channel.
Viterbi decoder is a “maximum likelihood” technique provides greater
improvement over the earlier complex methods (Akay and Ayanoglu,
2004). Convolutional encoding and Viterbi decoding (Forney,
1973) is an industry standard for all wireless channels. The concatenation
of two convolutional encoders and an interleaver and a simple decoding algorithm
revolutionized the coding field and their performances are very close to the
Shannon theoretical capacity limits Benedetto (2004).
Dos Santos et al. (2003) presented an insertion
/deletion detection and correcting decoding scheme for convolutional codes based
on the Viterbi decoding algorithm. Various concatenated Forward Error Correction
(FEC) codes on the performance of a wireless Orthogonal Frequency Division are
discussed by Haque et al. (2008) and Nyirongo
et al. (2006).
Mercier et al. (2010) summarized error correcting
codes for the channels that are perverted by synchronization errors and discussed
its applications as well as the obstacles needed to overcome. Adnan
and Masood (2011) made the comparison between uncoded and coded OFDM system
and analysed the (SER) Symbol Error Rate as a function of Signal to Noise Ratio(SNR),
with 1/2 rate convolution encoder and viterbi decoder has been analyzed and
is shown in Fig. 6.
Convolutional encoder is specified by (n, k, m) where n denotes the output
bits, k denotes the input bits and m denotes the memory registers (Seshadri
and Sundberg, 1994). The measure of efficiency of the code is called as
code rate k/n.

Fig. 6: 
Convolutional encoder (2,1), m: Message input, u1: First code
symbol, u2: Second code symbol, U: Output code word 
Constraint length L = k (m1) specifies the bits in the encoder memory that
influences the generation of output bits by adding superfluous bits:
gGenerator polynomial which symbolizes the bit selection to be combined that
contributes to the output bits (Blahut, 1985). Convolutional
encoder will take single or multibit input and generates encoded outputs. Begin
and Haccoun (1989) illustrates the various properties of convolutional codes.
Noise and other factors in wireless channels alter the bit sequences. By introducing
redundant bits, the original signal in presence of noise can be determined.
The most likely path of the transmitted sequence is computed by the Viterbi Algorithm using certain path metrics. Even in the presence of noise, the output will be the exact match of the input bits.
Reed Solomon (RS) codes: RS codes invented in 1960 by Reed and Solomon,
RS (n, k ) is a systematic non binary cyclic block code and is represented in
Fig. 7. These codes are based on Gaolis field where n = 2^{m}
1 and k = 2^{m} 12t (Blahut, 2002):
• 
n denotes the total symbols 
• 
k denotes the data symbols 
• 
t denotes the error correcting capability 
• 
For t = 2^{m} 1, RS codes can correct “ t “ or “
nk/2 “ symbols 
RS codes corrects a symbol with single bit error or even if all the bits in
the symbol are in error. It is best suited for correcting burst errors produced
by wireless channels. It is more sensitive to evenly spaced errors. RS codes
are called as Maximum Distance separable codes and the minimum distance of an
RS (n, k) code is nk+1. Let g(x) = (x+α) (x+α^{2}) (x+α^{2t
}) where g(x)= g0 +g1(x^{2}) + ….x^{2t
}g(x) represents the generator polynomial. M(x)= m_{0}(x) +m_{1}(x)
+ …….
M(x) denotes the message bits. Then perform x^{2t} m(x) / g(x)
x^{2t} m(x) = a(x) g(x) + b(x) where b(x )= b0(x) + b1(x)+……
b(x) is the remainder and
b(x) + x^{2t} m(x) is the codeword polynomial for the message.
Rs codes and Convolution codes are (Lee, 2005) the Coding
schemes in IEEE802.16a OFDM and presented in Table 3.
Turbo codes: Berrrou et al. (1993) introduced
a powerful new class of codes called Turbo codes which has been shown to perform
near the Shannon capacity limit in an AWGN channel. Schlegel
and Perez (2004) addresses turbo codes as parallel concatenated convolutional
codes.

Fig. 7: 
RS code representation 

Fig. 8: 
Representation of turbo code 
Table 3: 
Modulation and coding schemes in IEEE802.16a 

Wei (2004) and Hussain et al.
(2011) proposed concatenation using block and convolutional codes with RS
codes as the inner code and Convolutional codes as the outer code and they are
the most preferred codes for data communications and digital TV systems and
it’s diagrammatic representation is given in Fig. 8.
Turbo codes are formed by the parallel concatenation of two identical encoders
separated by an interleaver. Code word follows systematic form. The function
of the interleaver is to scramble the data input in a Psuedo random fashion.
Concatenated codes uses two levels of encoding one is the inner coding and other
is the outer coding (Benedetto and Montorsi, 1996).
The purpose of concatenated code is to achieve low probability of errors. The
inner code is mostly connected with Modulators and channels to correct the channel
errors and the outer codes reduces the error probability. Vafi
et al. (2009) presents Serially Concatenated Turbo codes which is
constructed as the serial combination of two turbo codes which outperform the
parallel concatenated turbo codes. Performances of the commonly used trellis
termination methods are compared and concluded that the performance depends
on the choice of the interleaver Hokfelt et al. (1999).
Afghah et al. (2008) proposes a new scheme of
fast turbo codes which aims at space diversity and coding gain by utilizing
turbo codes and Space time block codes as the inner and outer codes, respectively.
According to Lin et al. (1999), turbo codes
is being considered to enhance mobile wireless channel performance. In a coded
OFDM system with diversity to achieve high data rate has been explain by Muta
and Akaiwa (2006), Salari et al. (2008) and
Thenmozhi and Prithiviraj (2008). A similar approach
on diversity reception but for CDMA in mobile application is available in study
of Hemalatha et al. (2009).
NEURAL NETWORKS Nowadays neural networks are gaining momentum for multiple applications. It mainly reduces long design analysis for the development of highperformance systems. These networks are selforganized mathematical learning models basing on domain knowledge and have the capability for modeling in the most of uncertainty and noise. It is pretrained with several inputs and the error at the output is compared with the expected output for every session of training. Then the output layer is modified synchronously with the input layer, thereby reducing error rate and can be accomplished with lower complexity, faster convergence and offers superior BER performance capabilities when compared to the traditional means/schemes.
The artificial neuron was first introduced by McCullock
and Pitts (1943). It is a network made up of interconnected processing elements
called neurons. It has the ability to detect and extract complicated and imprecise
data that cannot be handled by Computers and human beings. The artificial neurons
learn by training to produce amazing results. Trained Neural network can be
Adaptive; self organised, operates in real time applications and is Fault tolerant.
The hypothesis of learning based on neural plasticity was proposed by Hebb
(1949) and is popularly called as unsupervised Hebbian learning rule. Later,
Farley and Clark (1954) simulated the Hebbian network
using computational machines. For other neural networks, computational machines
were made by Rochester et al. (1956).
Neural network model: Neural networks are made up of three layers namely
input layer, hidden layer and output layer with full interconnections between
them (Haykin, 1999). Input layer is passive and simply
takes a single input and produces multiple outputs is shown in Fig.
9.

Fig. 9: 
Neural network model 
Hidden and output layers are active, can modify the signal and take action
based on the weights applied. A two layer perceptron learning algorithm for
pattern recognition was created by Rosenblatt (1958).
The mathematical computation of the Exor circuit could not be performed using
the perceptron algorithm and was done through the back propagation algorithm
by Werbos (1974). Neural networks are more adaptive systems
that transform a vector from input to the corresponding vector at the output.
The neurons are characterized by internal threshold and by the type of activation
function. To accomplish desired mapping, the network should iterate with a change
in its internal parameters called the training process, until a set of parameters
is found which minimizes the error between the computed and the desired output
vector.
PAPR reduction techniques with neural networks: PAPR results in high
outofband emission called spectrum spreading and non linear distortion.
Van Nee and Prasad (2000) which is mainly due to the
large number of subcarriers in OFDM. Several PAPR reduction schemes have been
proposed. Signal distortion techniques (Li and Cimini, 1997)
like clipping, peak windowing and peak cancellation which reduce the peak amplitudes
by nonlinearly distorting the OFDM signal around the peak values have been analysed
by Van Nee and Prasad (2000) and Wang
et al. (1999). A prominent solution to reduce PAPR is by utilizing
coding techniques is given by Van Nee and Prasad (2000),
Larsen et al. (2004) and Paterson
and Tarokh (2000) which improves the bit error rate. The fluctuations are
given by PAPR = max p(t)/Pav where p(t) and pav represents the instantaneous
and average power of one OFDM symbol.
According to Davis and Jedwab (1999), Selective Mapping
(SLM) the transmit sequence is multiplied by the random sequence which is selected
to minimize PAPR of OFDM signal (Wilkinson and Jones, 1995).
In Partial transmit sequence (Hagenauer et al., 1996;
Pundiah, 1998) PAPR of the OFDM signal is reduced by
grouping all subcarriers into several clusters and adjusting the phase of each
cluster, symbolbysymbol, to minimize the PAPR (Tarokh
and Jafarkhani, 2000). Latif and Gohar (2008) used
a Hybrid QAMFSK OFDM transceiver which produces a reduction in PAPR compared
to Partial transmit sequence method of PAPR scheme by Latif
and Gohar (2003). Hassan and ElTarhuni (2011) made
a comparative study between SLM, modified SLM and PTS. All the techniques provide
improvement in PAPR reduction. As the phase sequences increases, the PAPR reduction
increases in the expense of complexity. Modified SLM outperforms the conventional
SLM. SLM has an improvement of 0.5 dB in PAPR reduction than that of PTS scheme.
PAPR reduction techniques with convolutional codes: Wang
et al. (2008) and Khan and Sheikh (2009)
discuss in detail to reduce PAPR in OFDM system, by employing SLM technique
with Convolutional codes and avoids the transmission of side information. PAPR
reduction using Convolutional coding employing PTS method is discussed (Verma
et al., 2011). 8ASK mapping based on SLM is presented and the results
show reduction in PAPR (Sichao and Dongfeng, 2005).
Standard convolution code (7, [171,133]) used in wireless systems is used and
provides reasonably good BER and PAPR reduction compared to other nonidentical
polynomial codes (Vallavaraj et al., 2006). Terminated
convolutional codes with offset for PAPR reduction is given by Chen
et al. (2003). The convolutional codes which can be easily decoded
by using the Viterbi algorithm, have low PAPR and acceptable code rates. The
peak to average power ratio of convolutional coded OFDM signals can be significantly
degraded when compared with uncodedOFDM. This degradation occurs for code rates
R<1/2 and relatively low constraint lengths (Frontana
and Fair, 2007).
PAPR reduction techniques with TURBO CODES: Muta
and Akaiwa (2006) entails an exhaustive search for low PAPR in OFDM and
proposes a weighting factor method. In this method, without using any side information
turbo codes are capable of error correction and also estimating the weighting
function. They extended their estimation using PTS in (Muta
and Akaiwa, 2008). Sabbaghian et al. (2011)
propose of a timefrequency turbo block code to achieve better BER with a low
PAPR close to the Shannon limit. Tsai and Ueng, (2007)
has given a way to achieve low PAPR and higher BER, authors employs tailbiting
turbo code to generate multiple candidates using SLM which results in RS codes
similar to the conventional one excluding 1,2 of RS codes in tailbit form.
The tailbiting codeword starts and ends in the same state. To mitigate peak
power problem in OFDM three turbo code OFDM systems are introduced by Lin
et al. (2003). In the first method short codes are used to protect
the side information and long maximum length sequences are used as test sequences.
This results in protection of the side information by increasing the power of
subcarriers. In the Second method, no side information is required. It employs
various interweavers to produce output with various PAPR and selects the one
with the lowest PAPR. The third method employs the combination of one and two
and method three has better BER performance and higher transmission rate and
LOW PAPR .
PAPR reduction techniques with RS codes: In contrast to the existing
approaches to reduce PAPR in OFDM, RS codes and simplex codes are arranged over
the frames of OFDM and pick out the best one which provides low PAPR (Fischer
and Siegl, 2009). RSOFDM is analysed over Rayleigh fading channels with
Additive White Gaussian Noise (AWGN). It is the combination of ReedSolomon
(RS) codes and Orthogonal Frequency Division Multiplexing (OFDM), in which RS
code operates as the OFDM frontend. Van Meerbergen et
al. (2006a) provides low Peak to Average Power Ratio (PAPR) and removes
ISI by Gaolis field equalizer. It also provides better results compared to traditional
coded OFDM. Van Meerbergen et al. (2006b) and
Fischer and Siegl (2008) presents a new design solution
for low PAPR in presence of impulse noise. The problem is tackled by decomposing
the circular channel matrix into parallel channels by using DFT matrices in
a Galois field of odd characteristic, rather than in a complex field. OFDM merged
with a ReedSolomon (RS) code, with its maximal Hamming distance is preferred
for impulse noise cancellation.
OFDM USING NEURAL NETWORKS
OFDM pulse shape generation using ANN is discussed by Akah
et al. (2009). Necmi and Nuri (2010) uses
Multilayered Perceptrons (MLP) with Back Propagation (BP) learning algorithm
as a channel estimator for OFDM systems. A comparison between neural based channel
estimator with Least Square (LS) algorithm, Minimum mean Square Error (MMSE)
algorithm and Radial Basis Function neural network (RBF) was analysed with respect
to Bit Error Rate (BER) and Mean Square Error (MSE). From the analysis MLP neural
network has better performance than the others and provides better channel estimation.
Multilayered Perceptrons (MLP) based ACE (Active Constellation Expansion) to
reduce fluctuations in power envelope of OFDM signal was studied (Jabrane
et al., 2010). Charalabopoulos et al.
(2003) proposed a Radial Basis Function (RBF) neural network which are used
to provide channel equalization to combat the frequency selective fading in
OFDM systems. Mizutani et al. (2007) uses Hopfield
neural network and Back propagation Neural networks in order to provide reduction
in PAPR without the necessity of the side information required in other systems.
According to Chen et al. (2007), equalizer is
built using Back propagation algorithm and learning of the network is done through
MLP method which outperforms than the conventional equalizer. Learning of neural
network is done through MLP and the equalizer is based on Back Propagation algorithm
and yields better performance than the conventional equalizer. Louet
et al. (2004) used neural networks to compensate the nonlinear effects
in OFDM created by high power amplifiers and thus eliminates the peak factor
problem. Fischer and Siegl (2009), focuses on the Maximum
Distance separable code property of RS codes to achieve reduction in PAPR. Wang
et al. (2004) compares PAPR and carrier frequency offset between
OFDM and singlecarrier system with zero padding and justified that ZP is preferred
when code rate is high and OFDM is preferred for lower code rates. According
to Pei et al. (2010), concentrates on the resource
allocation for OFDM based system considering mutual interference using the Genetic
algorithm approach.
CONCLUSION OFDM is thus used to overcome the bandwidth constraint and provide better SNR. Its implementation and the problems associated with it are explained in detail. Pros and cons of OFDM and its wireline, wireless applications have been listed. Three types of error correcting codes called Convolutional codes, RS codes and Turbo codes have been illustrated with necessary theory and enumerated its weakness. It is also discussed as to how these problems can be overcome by the use of error control codes and neural networks. The various error code generation techniques have been explained. A detailed survey has been carried out to on PAPR reduction techniques using Neural Networks and Error Correcting Codes.

REFERENCES 
1: Adnan, T. and A. Masood, 2011. Use of convolution coding for improving SER performance of OFDM system. Proceedings of the 3rd IEEE International Conference on Communication Software and Networks, May 2729, 2011, School of Electronic Engineering University of New South Wales, Sydney, NSW, Australia, pp: 4043..
2: Akay, E. and E. Ayanoglu, 2004. High performance Viterbi decoder for OFDM systems. Proc. IEEE Vehicular Technol. Conf., 1: 323327. CrossRef 
3: Akansu, A.N., P. Duhamel, X.M. Lin and M. de Courville, 1998. Orthogonal transmultiplexers in communication: A review. IEEE Trans. Signal. Process., 46: 979995. CrossRef  Direct Link 
4: Akah, H.M., A. Kamel and H.M. ElHennawy, 2009. OFDM pulse shape generation using artificial neural networks. Proceedings of the IEEE EUROCON, May 1823, 2009, Natiional Authority of Remote Sensing and Space Science, Cairo, Egypt, pp: 16941699.
5: Amirtharajan, R., K. Thenmozhi and R.J.B. Balaguru, 2010. Multi carrier steg against omni attacks. Int. J. Comput. Applic., 5: 3540. Direct Link 
6: Arioua, M., S. Belkouch and M.M. Hassani, 2012. Efficient 16points FFT/IFFT architecture for OFDM based wireless broadband communication. Inf. Technol. J., 11: 118125. CrossRef  Direct Link 
7: Latif, A. and N.D. Gohar, 2008. On the PAPR reduction properties of hybrid QAMFSK (HQFM) OFDM transceiver. J. Applied Sci., 8: 10611066. CrossRef  Direct Link 
8: Bahai, A.R.S., B.R. Saltzberg and M. Ergen, 2004. MultiCarrier Digital Communications: Theory and Applications of OFDM. 2nd Edn., Springer, USA., ISBN13: 9781441935502.
9: Blahut, R.E., 1985. Algebraic fields, signal processing and error control. Proc. IEEE, 73: 874893. CrossRef  Direct Link 
10: Begin, G. and D. Haccoun, 1989. Highrate punctured convolutional codes: Structure properties and construction technique. IEEE Trans. Commun., 37: 13811385. CrossRef  Direct Link 
11: Benedetto, S. and G. Montorsi, 1996. Unveiling turbo codes: Some results on parallel concatenated coding schemes. IEEE Trans. Inform. Theory, 42: 409428. CrossRef  Direct Link 
12: Benedetto, S., 2004. Advanced error correcting coding techniques and iterative decoding. Proceedings of the 1st International Symposium on Control, Communications and Signal Processing, September 27, 2004, Politecnico di Torino, Italy, pp: 179179.
13: Berrrou, C., A. Glavieux and O. Thitimajshima, 1993. Near Shannon limit errorcorrecting coding and decoding: Turbocodes. Proceedings of the IEEE International Conference on Communication, May 2326, 1993, Geneva, Switzerland, pp: 10641070.
14: Bingham, J.A.C., 1990. Multicarrier modulation for data transmission. An idea whose time has come. IEEE Commun. Mage., 28: 514. CrossRef  Direct Link 
15: Blahut, R.E., 2002. Algebraic Codes for Data Transmission. Cambridge University Press, Cambridge, UK., ISBN13: 9780521553742.
16: Chang, R. and R. Gibby, 1968. A theoretical study of performance of an orthogonal multiplexing data transmission scheme. IEEE Trans. Commun. Technol., 16: 529540. CrossRef  Direct Link 
17: Chang, R.W., 1970. Orthogonal frequency division multiplexing. U.S. Patent No. 3488445.
18: Casas, E.F. and C. Leung, 1991. OFDM for data communication over mobile radio FM channels. I. Analysis and experimental results. IEEE Trans. Commun., 39: 783793. CrossRef  Direct Link 
19: Cimini, L.J., 1985. Analysis and simulation of a digital mobile channel using orthogonal frequency division multiplexing. IEEE Trans. Commun., 33: 665675. CrossRef  Direct Link 
20: Cimini Jr., L.J., B. Daneshrad and N.R. Sollenberger, 1996. Clustered OFDM with transmitter diversity and coding. IEEE Global Telecommun. Conf., 1: 703707. CrossRef 
21: Charalabopoulos, G., P. Stavroulakis and A.H. Aghvami, 2003. A frequencydomain neural network equalizer for OFDM. IEEE Global Telecommun. Conf., 2: 571575. CrossRef  Direct Link 
22: Chen, E., R. Tao and X. Zhao, 2007. Channel equalization for OFDM system based on the BP neural network. Proceedings of the 8th International Conference on Signal Processing, April 10, 2007, Beijing Institute of Technology, Beijing .
23: Chen, C.Y., C.H. Wang and C.C. Chao, 2003. Convolutional codes for peaktoaverage power ratio reduction in OFDM. Proceedings of theIEEE International Symposium on Information Theory, 29 June4 July 2003, National Tsing Hua University, Hsinchu, Taiwan, pp: 55.
24: Chung, J.C., 1987. The effect of time delay spread on portable radio communications channels with digital modulation. IEEE J. Selected Areas Commun., 5: 879889. Direct Link 
25: Davis, J.A. and J. Jedwab, 1999. Peaktomean power control in OFDM, Golay complementary sequences and ReedMuller codes. IEEE Trans. Inform. Theory, 45: 23972417. CrossRef  Direct Link 
26: Doelz, M.L., E.T. Heald and D.L. Martin, 1957. Binary data transmission techniques for linear systems. Proc. IRE, 45: 656661. CrossRef  Direct Link 
27: Wang, D., X.G. Xia and J. Zhang, 2008. A novel peaktoaverage power ratio reduction method for coded OFDM systems. Proceedings of the IEEE International Symposium on Broadband Multimedia Systems and Broadcasting, March 31April 2, 2008, Philips Research, Briarcliff Manor, NY USA., PP: 15.
28: Dos Santos, M.P.F., W.A. Clarke, H.C. Ferreira and T.G. Swart, 2003. Correction of insertions/deletions using standard convolutional codes and the Viterbi decoding algorithm. Proceedings of the IEEE workshop on Information Theory, March 31April 4, 2003, Rand Afrikaans University, South Africa, pp: 187190.
29: Elahmar, S., A. Djebbari, M. Bouziani and J.M. Rouvaen, 2007. New results with blind time domain equalization for OFDM system. Inform. Technol. J., 6: 207211. CrossRef  Direct Link 
30: Elias, P., 1958. Computation in the presence of noise. IBM J. Res. Dev., 2: 346353. CrossRef  Direct Link 
31: Farley, B. and W. Clark, 1954. Simulation of selforganizing systems by digital computer. IRE Trans. Inform. Theory, 4: 7684. CrossRef  Direct Link 
32: Afghah, F., M. Ardebilipour and A. Razi, 2008. Fast turbo codes concatenated with spacetime block codes. J. Applied Sci., 8: 28672873. CrossRef  Direct Link 
33: Fischer, R.F.H. and C. Siegl, 2008. Peaktoaverage power ratio reduction in OFDM using reedsolomon codes. Proceedings of the IEEE International Zurich Seminar on Communications, March 1214, 2008, Zurich, Switzerland, pp: 4043.
34: Fischer, R.F.H. and C. Siegl, 2009. Reedsolomon and simplex codes for peaktoaverage power ratio reduction in OFDM. IEEE Trans. Inform. Theory, 55: 15191528. CrossRef 
35: Forney, Jr. G.D., 1970. Convolutional codes I: Algebraic structure. IEEE Trans. Inform. Theory, 16: 720738. CrossRef 
36: Forney, Jr. G.D., 1971. Burstcorrecting codes for the classic bursty channel. IEEE Trans. Commun. Technol., 19: 772781. CrossRef 
37: Forney, G.D., 1973. The viterbi algorithm. Proc. IEEE, 61: 268278. CrossRef  Direct Link 
38: Frontana, E. and I. Fair, 2007. Avoiding PAPR degradation in convolutional coded OFDM signals. Proceedings of the IEEE Pacific Rim Conference on Communications, Computers and Signal Processing, August 2224, 2007, Victoria, Canada, pp: 312315.
39: Hussain, G.A., M.B. Mokhtar and R.S.A.B. Raja, 2011. Concatenated RSconvolutional codes for MIMOOFDM system. Asian J. Applied Sci., 4: 720727. CrossRef  Direct Link 
40: Hassan, Y. and M. ElTarhuni, 2011. A comparison of SLM and PTS peaktoaverage power ratio reduction schemes for OFDM systems. Proceedings of the 4th International Conference on Modeling, Simulation and Applied Optimization, April 1921, 2011, Kuala Lumpur, Malaysia, pp: 14.
41: Hagenauer, J., E. Offer and L. Papke, 1996. Iterative decoding of binary block and convolutional codes. IEEE Trans. Inform. Theory, 42: 429445. CrossRef 
42: Liu, H., H. Zhong, T. Zhang and Z. Gong, 2006. A quasinewton acceleration EM algorithm for OFDM systems channel estimation. Inf. Technol. J., 5: 749752. CrossRef  Direct Link 
43: Haque, M.D., S.E. Ullah and M.R. Ahmed, 2008. Performance evaluation of a wireless orthogonal frequency division multiplexing system under various concatenated FEC channelcoding schemes. Proceedings of the 11th International Conference on Computer and Information Technology, December, 2427, 2008, Bangladesh, pp: 9497.
44: Hebb, D.O., 1949. The Organization of Behavior:A Neuropsychological Theory. 1st Edn., Wiley, New York, ISBN: 0805843000.
45: Hemalatha, M., K. Thenmozhi, V. Prithiviraj, D. Bharadwaj and R. Vignesh, 2009. Diversity reception for CDMA based mobile communication systems. Proceedings of the 1st International Conference on Wireless Communication, Vehicular Technology, Information Theory and Aerospace and Electronic Systems Technology, May 1720, 2009, Aalborg, pp: 660664.
46: Holsinger, J., 1964. Digital communication over fixed timecontinuous channel with memoryWith special application to telephone channels. Ph.D. Thesis, Massachusetts Institute of Technology, Cambridge, MA., USA.
47: Hirosaki, B., 1981. An orthogonally multiplexed QAM system using the discrete fourier transform. IEEE Trans. Commun., 29: 982989. Direct Link 
48: Hokfelt, J., O. Edfors and T. Maseng, 1999. A survey on trellis termination alternatives for turbo codes. IEEE Veh. Technol. Conf., 323: 22252229. CrossRef 
49: AlKebsi, I.I.M., 2008. The impact of modulation adaptation and power control on peak to average power ratio clipping technique in orthogonal frequency division multiplexing of fourth generation systems. J. Applied Sci., 8: 27762780. CrossRef  Direct Link 
50: Jabrane, Y., V.P.G. Jimenez, A.G. Armada, B.A.E. Said and A.A. Ouahman, 2010. Reduction of power envelope fluctuations in OFDM signals by using neural networks. IEEE Commun. Lett., 14: 599601. CrossRef 
51: Kalet, I., 1989. The multitone channel. IEEE Trans. Commun., 37: 119124. CrossRef  Direct Link 
52: Khan, K. and S.A. Sheikh, 2009. PAPR reduction of OFDM signals using convolutional codes. Proceedings of the IEEE Student Conference on Research and Development, November 1618, 2009, UPM, Serdang, Malaysia, pp: 2628.
53: Kumar, R., S. Malarvizhi and S. Jayashri, 2008. Timedomain equalization technique for intercarrier interference suppression in OFDM systems. Inform. Technol. J., 7: 149154. CrossRef  Direct Link 
54: Kumar, P.P., R. Amirtharajan, K. Thenmozhi and J.B.B. Rayappan, 2011. StegOFDM blend for highly secure multiuser communication. Proceedings of the 2nd International Conference on Vehicular Technology, Information Theory and Aerospace and Electronic Systems Technology, February 28March 3, 2011, Chennai, India, pp: 15.
55: Latif, A. and N.D. Gohar, 2003. Reducing peaktoaverage power ratio (PAPR) using partial transmit sequence in OFDM systems. Proceedings of the 7th International Conference on Multi Topic, December 89, 2003, IEEE Computer Society, PP: 126130.
56: Wei, L., 2004. Iterative Viterbi algorithm: implementation issues. IEEE Trans. Wireless Commun., 3: 382386. CrossRef  Direct Link 
57: Louet, Y., S. Tertois and P. Barreau, 2004. Reducing nonlinear OFDM signal distortions using neural networks in the time domain. Proceedings of the Internation. Conf. on Information and Communication Technologies, From Theory to Applications, April 1923, 2004, Omayyad Palace, Damascus, pp: 267268.
58: Larsen, Y., G. Leus and G.B. Giannakis, 2004. Constant modulus and reduced PAPR block differential encoding for frequencyselective channels. IEEE Trans. Commun., 52: 622631. CrossRef 
59: Lin, L., L.J. Cimini and J.C.I. Chuang, 1999. Turbo codes for OFDM with antenna diversity. IEEE Veh. Technol. Conf., 2: 16641668. CrossRef 
60: Sichao, L. and Y. Dongfeng, 2005. Reducing PAPR of OFDM with convolutional code and 8ask mapping. Proceedings of the International Conference on Wireless Communications, Networking and Mobile Computing, September 2326, 2005, China, pp: 253256.
61: Lin, M.C., K.C. Chen and S.L. Li, 2003. Turbo coded OFDM system with peak power reduction. IEEE Veh. Technol. Conf., 4: 22822286. CrossRef 
62: Mercier, H., V.K. Bhargava and V. Tarokh, 2010. A survey of errorcorrecting codes for channels with symbol synchronization errors. IEEE Commun. Surv. Tutorials, 12: 8796. CrossRef 
63: Mizutani, K., M. Ohta, Y. Ueda and K. Yamashita, 2007. A PAPR reduction of OFDM signal using neural networks with tone injection scheme. Proceedings of the 6th International Conference on Information, Communications and Signal Processing, December 1013, 2007, Singapore, pp: 15.
64: Muta, O. and Y. Akaiwa, 2006. A weighting factor estimation scheme for phasecontrol based peak power reduction of turbocoded OFDM signal. Proceedings of the IEEE Vehicular Technology Conference, May 710, 2006, Melbourne, pp: 14771481.
65: Muta, O. and Y. Akaiwa, 2008. Iterative weighting factor estimation method for peak power reduction with adaptive subcarrierphase control in turbocoded multicarrier CDM Systems. Proceedings of the IEEE 68th Vehicular Technology Conference, September 2124, 2008, Calgary, pp: 15.
66: Nyirongo, N., W.Q. Malik and D.J. Edwards, 2006. Concatenated RSconvolutional codes for ultrawideband multibandOFDM. Proceedings of the IEEE International Conference on UltraWideband, September 2427, 2006, Waltham, MA., USA., pp: 137142.
67: Omura, J., 1969. On the Viterbi decoding algorithm. IEEE Trans. Inform. Theory, 15: 177179. CrossRef 
68: Paterson, K.G. and V. Tarokh, 2000. On the existence and construction of good codes with low peaktoaverage power ratios. Proceedings of the IEEE International Symposium on Information Theory, June 2530, 2000, Sorrento, pp: 217.
69: Peled, A. and A. Ruiz, 1980. Frequency domain data transmission using reduced computational complexity algorithms. Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing, April 1924, 1980, Taipei, Taiwan, pp: 964967.
70: Venkatesan, G.K.D.P. and V.C. Ravichandran, 2007. Performance analysis of MCCDMA for wide band channels. Inform. Technol. J., 6: 267270. CrossRef  Direct Link 
71: Pundiah, R.M., 1998. Near optimum decoding of product codes. IEEE Trans. Comm., 4: 10031010. CrossRef  Direct Link 
72: Rappaport, T.S., A. Annamalai, R.M. Buehrer and W.H. Tranter, 2002. Wireless communications: Past events and a future perspective. IEEE Commun. Maga., 40: 148161. CrossRef  Direct Link 
73: Rochester, N., J. Holland, L. Habit and W. Duda, 1956. Tests on a cell assembly theory of the action of the brain, using a large digital computer. IRE Transact. Inf. Theory, 2: 8093. CrossRef 
74: Rosenblatt, F., 1958. The perceptron: A probabilistic model for information storage and organization in the brain. Psych. Rev., 65: 386408. CrossRef  PubMed  Direct Link 
75: Sabbaghian, M., Y. Kwak, B. Smida and V. Tarokh, 2011. Near shannon limit and low peak to average power ratio turbo block coded OFDM. IEEE Trans. Commun., 59: 20422045. CrossRef 
76: Salari, S., M. Ardebilipour and M. Ahmadian, 2008. Channel and frequency offset estimation for MIMOOFDM systems. J. Applied Sci., 8: 809815. CrossRef  Direct Link 
77: Saltzberg, B., 1967. Performance of an efficient parallel data transmission system. IEEE Trans. Commun. Technol., 15: 805811. CrossRef  Direct Link 
78: Seddiki, A., A. Djebbari, J.M. Rouvaen and A. TalebAhmed, 2006. BCH coding performance evaluation on a land mobile channel based OFDM system. Inform. Technol. J., 5: 930936. CrossRef  Direct Link 
79: Seshadri, N. and C.E.W. Sundberg, 1994. List Viterbi decoding algorithms with applications. IEEE Trans. Commun., 42: 313323. CrossRef 
80: Lee, S.G., 2005. Performance of concatenated FEC under fading channel in wirelessMAN OFDM system. Proc. 19th Int. Conf. Adv. Inf. Network. Applic., 1: 781785. CrossRef  Direct Link 
81: Haykin, S., 1999. Neural Networks a Comprehensive Foundation. PrenticeHall, New Jersey.
82: Speth, M., S.A. Fechtel, G. Fock and H. Meyr, 1999. Optimum receiver design for wireless broadband systems using OFDM. I. IEEE Trans. Commun., 47: 16681677. CrossRef  Direct Link 
83: Schlegel, C.B. and L.C. Perez, 2004. Trellis and Turbo Coding. WileyIEEE Press, New Jersey, Pages: 386.
84: Tarokh, V. and H. Jafarkhani, 2000. On the computation and reduction of the peaktoaverage power ratio in multicarrier communications. IEEE Trans. Commun., 48: 3744. CrossRef  Direct Link 
85: Necmi, T. and S.M. Nuri, 2010. Back propagation neural network approach for channel estimation in OFDM system. Proceedings of the IEEE International Conference on Wireless Communications, Networking and Information Security, June 2527, 2010, Beijing, China, pp: 265268.
86: Thenmozhi. K., 2008. Studies on orthogonal frequency division multiplexing (OFDM) implementation at the physical layer on a wireless platform. Ph.D. Thesis, SASTRA University India.
87: Thenmozhi, K., R. Varadarajan, V. Prithiviraj and S. Shweta, 2006. MCCDMA promises wireless broad band beyond 3G. Elect. Eng. Times Asia, pp: 13, http://www.eetindia.co.in/ARTICLES/2006AUG/PDF/EEIOL_2006AUG28_RFD_TA.pdf.
88: Thenmozhi, K., V.K. Konakalla, S.P.P. Vabbilisetty and R. Amirtharajan, 2011. Space Time Frequency coded (STF) OFDM for broadband wireless communication systems. J. Theor. Applied Inform. Technol., 3: 5359. Direct Link 
89: Thenmozhi, K. and V. Prithiviraj, 2008. Suitability of Coded Orthogonal Frequency Division Multiplexing (COFDM) for multimedia data transmission in wireless telemedicine applications. Conf. Comput. Intelli. Multimedia Appl., 4: 288292. CrossRef 
90: Van Nee, R. and R. Prasad, 2000. OFDM for Wireless Multimedia Communications. Artech House, Norwell, MA., USA., ISBN13: 9780890065303, Pages: 260.
91: Vallavaraj, A., G.S. Brian, K.H. David and G.M. Francis, 2006. Optimizing the rate 1/2; convolutional code for OFDM applications in terms of biterrorrate and peaktoaverage power ratio. Proceedings of the IEEE GCC Confrrence, March 2022, 2006, Manama, pp: 16.
92: Vafi, S., T. Wysocki and M. Abolhasan, 2009. Serially concatenated turbo codes. Proceedings of the 5th International Conference on Wireless Communications, Networking and Mobile Computing, September 2426, 2009, Beijing, China, pp: 14.
93: Van Meerbergen, G., M. Moonen and M. De Man, 2006. Reedsolomon codes implementing a coded OFDM scheme for rayleigh fading channels. Proceedings of the Global Telecommunications Conference IEEE, Nov. 27 Dec. 1, San Francisco, CA, pp: 16.
94: Van Meerbergen, G., M. Moonen and H. de Man, 2006. Combining reedsolomon codes and ofdm for impulse noise mitigation: RSOFDM. Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing, May 1419, 2006, Toulouse, .
95: Verma, S., P. Sharma, S. Ahuja and P. Hajela, 2011. Partial transmit sequence with convolutional codes for reducing the PAPR of the OFDM signal. Proceedings of the 3rd International Conference Electronics Computer Technology, April 810, 2011, Kanyakumari, pp: 7073.
96: Viterbi, A., 1967. Error bounds for convolutional codes and an asymptotically optimum decoding algorithm. IEEE Trans. Inform. Theor., 13: 260269. Direct Link 
97: Weinstein, S. and P. Ebert, 1971. Data transmission by frequencydivision multiplexing using the discrete fourier transform. IEEE. Trans. Commun., 19: 628634. CrossRef  Direct Link 
98: Jiang, W., Z. Zhang, Y. Xu and L. Sun, 2010. Dynamic intercell interference cancellation for uplink in multicell OFDMA systems. Inform. Technol. J., 9: 14901494. CrossRef  Direct Link 
99: Wilkinson, T.A. and A.E. Jones, 1995. Minimisation of the peak to mean envelope power ratio of multicarrier transmission schemes by block coding. Vehicular Technol. Conf., 2: 825829. CrossRef 
100: Willink, T.J. and P.H. Wittke, 1997. Optimization and performance evaluation of multicarrier transmission. IEEE Trans. Infor. Theory, 43: 426440. CrossRef  Direct Link 
101: Wulich, D., 2005. Definition of efficient PAPR in OFDM. IEEE Commun. Lett., 9: 832834. CrossRef  Direct Link 
102: Werbos, P.J., 1974. Beyond regression: New tools for prediction and analysis in behaviour sciences. Ph.D. Thesis, Harvard University, Cambridge, Mass.
103: Wang, X., T.T. Tjhung and C.S. Ng, 1999. Reduction of peaktoaverage power ratio of OFDM system using a companding technique. IEEE Trans. Broadcast., 45: 303307. CrossRef  Direct Link 
104: Tsai, Y.C. and Y.L. Ueng, 2007. A tailbiting turbo coded OFDM system for PAPR and BER reduction. Proceedings of the 66th Vehicular Technology Conference, September 30October 3, 2007, Baltimore, pp: 10671071.
105: Zimmerman, M. and A. Kirsch, 1967. The AN/GSC10 (KATHRYN) variable rate data modem for HF radio. IEEE Trans. Commun. Technol., 15: 197204. CrossRef  Direct Link 
106: Wang, Z., X. Ma and G.B. Giannakis, 2004. OFDM or singlecarrier block transmissions. IEEE Trans. Commun., 52: 380394. CrossRef  Direct Link 
107: Zou, W.Y. and Y. Wu, 1995. COFDM: An overview. IEEE Trans. Broadcast, 41: 18. CrossRef  Direct Link 
108: Li, X. and L.J. Cimini, 1997. Effects of clipping and filtering on the performance of OFDM. Proceedings of the IEEE 47th Vehicular Technology Conference, May 45, Phoenix, AZ. USA., pp: 16341638.
109: McCulloch, W.S. and W. Pitts, 1943. A logical calculus of the ideas immanent in nervous activity. Bull. Math. Biophys., 5: 115133. CrossRef  Direct Link 
110: PeiPei, C., Z. QinYu, W. Ye and M. Jing, 2010. Multiobjective resource allocation for OFDMbased cognitive radio systems. Inform. Technol. J., 9: 494499. CrossRef  Direct Link 



