INTRODUCTION
User cooperation in wireless networks is an effective technique that enables
users to cooperate with each other in their transmissions, thus increasing the
transmission efficiency. Relay channels are a special class of cooperative transmission
networks, where a source wishes to transmit a message to a destination with
the help of relays. The information theoretic study of relay channels have been
broadly investigated (Cover and Gamal, 1979; Kramer
et al., 2005; HostMadsen and Zhang, 2005;
Reznik et al., 2004; Paulraj
et al., 2003; Wang et al., 2005)
and practical relaying protocols have also been developed (Laneman
et al., 2004).
Van Der Meulen (1971) was the first one who introduced
the relay channel. This channel model was then studied deeply by Cover
and Gamal (1979). Up to now, the studies on relay channels have been expanded
to largescale hybrid networks, for example (1) The wireless sensor networks
(Youn and Kang, 2008; Shakir and
Wang, 2008; Arivubrakan and Dhulipala, 2013), (2)
The multiway relay networks (Ong et al., 2011,
2012; Timo et al., 2013)
and (3) The LTEadvanced networks (Sasikala and Srivatsa,
2006; Abed et al., 2011). In these relay
modes, the relay nodes only assist the source with relaying messages to the
destination without sending new messages of their own. When the traditional
relay channel is applied to a practical large network, in order to make full
use of the channel capacity, one has to consider the capacity limits if a relay
node must play a role both in relaying the source messages, as well as its own
messages. A representative channel model is proposed as illustrated in Fig.
1 which is referred to as Relay Channel with Forwarding Own Messages (RCFOM).
This RCFOM consists of a pointtopoint communication channel between the relay
and the destination and relayed channels in comparison with the traditional
relay channel.
In this study, the new channel model is established and the impact of the relay
with forwarding own messages on capacity limits on upper bounds is studied.
By proposing the random coding method with jointly typical sequences, achievable
rates for both the discrete memoryless and Gaussian RCFOM are derived. Finally,
the achievable rate regions under different channel conditions are compared
and validated by simulations.

Fig. 1: 
Information flow of relay channel with forwarding own messages 
MATERIALS AND METHODS
Experimental system model: The relay channel is a threeterminal discrete
memoryless channel consisting of finite sets denoted by X_{1}, X_{2},
Y_{1}, Y_{2} (i.e., cardinalities of random variables X_{1},
X_{2}, Y_{1} and Y_{2}) and a transition probability
distribution p(y_{1},y_{2}x_{1},x_{2}) where
x_{1}εX_{1}, x_{2}εX_{2}, y_{1}εY_{1}
and y_{2}εY_{2}. In this channel, X_{1} and X_{2}
are the channel inputs from the source and the relay, respectively while Y_{1}
and Y_{2} are the channel outputs at the relay and destination, respectively.
This channel was described by Van Der Meulen (1971)
as the first work on the achievable rate regions for the relay channel. Different
cooperation schemes such as DecodeandForwarding (DF) and CompressandForwarding
(CF) were introduced. However, the relay can also send independent and new messages
in addition to relaying messages that help the destination in decoding the source's
message. This novel system model is named as the relay channel with forwarding
own messages in this study. Correspondingly, the relay uses DF scheme as the
transmission strategy.
A
code for the RCFOM consists of the following:
• 
Two sets of integers, the source message
and the relay message 
• 
An encoder at the transmitter, X_{1}: W_{1}→X_{1}^{n}
where, X^{i}_{j}(X_{i,1},
X_{i,2},... X_{i,j}) 
• 
A set of relay functions {f_{i}}^{n}_{i = 1} at
the relay such that: 

where, x_{2,i } is the ith component of the codeword
x_{2} = (x_{2,1},... x_{2,n}) that is only dependent
of the past received information (y_{1,1},... y_{1,i1})
and the information w_{o} 
• 
A decoder at the destination, φ: Y^{n}→W_{1}xW_{0} 
The average error probability of decoding W_{1} and W_{0} is
defined as:
Figure 2 illustrates the encoding and decoding structure
of the two messages.
denote the estimates of W_{1} and W_{o}. The source and the
relay generate their messages (W_{1}, W_{o}) independently and
uniformly over W_{1}xW_{0}.
A rate pair (R_{1}, R_{o}) is said to be achievable for the
RCFOM if there exist a sequence of codes
such that for any ò>0, the average probability of error:
as n→∞.
A relay channel with forwarding own messages is said to be degraded if its
transition probability satisfies:
That is to say, Y_{2} is independent of X_{1} on the condition
of having Y_{1} and X_{2}. Note that the definition of degradation
precisely describes the notation that one channel is worse than other one in
the RCFOM.
General method: In this subsection, the result of the maxflowmincut
theorem by Cover and Thomas (1991) is used as a method
to establish upper rate bounds on the capacity region of the RCFOM.
Given any
code for RCFOM, the joint probability distribution satisfies:
According to Fano’s inequality,
the information entropy H(W_{1}, W_{0}Y_{2}) can be
bounded as:

Fig. 2: 
The encoding and decoding process for the relay channel with
forwarding own messages 
As the message can be decoded from Y_{2}, P^{n}_{e}→0
and δ_{n} defined as (R_{1}+R_{o})P^{n}_{e}+1/n,
also goes to zero as n→∞.
In the following, R_{1} is upper bounded as:
where, Eq. 89 follow as conditioning reduces
entropy. Now, let Q be a random variable uniformly distributed over {1,...,n},
set V_{1} = QY^{i}_{1,i+1}W_{1}, V_{2}
= QY^{i1}_{2}, Y_{1} = Y_{1,Q}, Y_{2}
= Y_{2,Q}.
Hence:
Also:
Hence:
Then, for the relaydestination channel, R_{o} can be bounded easily
as below:
Based on the derivation of the upper bounds in Eq. 10, 12
and 13 by taking n→∞, this subsection draws a
conclusion. For any rate pair (R_{1}, R_{o}) with P^{n}_{e}→0
of the RCFOM, there exist some random variables U→(V_{1}, V_{2})→(X_{1},
X_{2})→(Y_{1}, Y_{2}), such that (R_{1},
R_{o}) satisfies the following conditions:
PROPOSED APPROACH
Here, proposes a random coding technique with jointly typical sequences to
derive the achievable rate region for the RCFOM based on the wellknown DF
strategy (Cover and Gamal, 1979). Here, the relay is
assumed to be able to fully recover the source’s message forwarded to the
destination. Then, it reencodes the decoded source message W_{1} together
with its own message W_{o} for the destination.
The coding schemes combine ideas from the relay channel (Cover
and Gamal, 1979), the broadcast channel (Liang and
Veeravalli, 2007) and the multiple access channel (Willems,
1982).
Random codebook generation:
• 
Randomly generated independently and identically distributed
(i.i.d) nsequence u with probability: 
Label them as u(w’_{1}).
Assume that all the nodes know u
• 
For each u(w’_{1}) generate
conditionally independent nsequence x_{1} at the source each drawn
randomly according to: 
index them as
• 
For each u(w’_{1}) generate at random
i.i.d nsequence x_{2} at the relay, each with distribution: 
index them as
Assume a transmission period of B blocks, each consisting of n transmissions.
A sequence of B1 i.i.d source messages
iε[1:B1] and a sequence of B1 i.i.d relay messages
iε[1:B1], are to be sent over the channel in nB transmissions, respectively.
Note that the average rate pairs over B blocks are:
which can be made as close to (R_{1}, R_{o}) as desired when
B→∞. The encoding and decoding are explained with the help of Table
1.
Encoding: At first consider block i, where i ≠ 1, B which means it
is not the first or the last block:
• 
The encoder at the source sends x_{1}(w_{1}(i),
w_{1}(i1)), where w_{1}(i1) was denoted above as w’_{1} 
• 
Assuming that the relay already has a correct estimation of w_{1}(i1)
from the previous block, then it sends x_{2}(w_{0}(i), w_{1}(i1)) 
When i = 1, the source sends x_{1}(w_{1}(1), 1) and the relay
sends x_{2}(w_{0}(1)1), where w_{1}(0) = 1 by convention.
When i = B, the source sends x_{1}(1, w_{1}(B1)) and the relay
sends x_{2}(1, w_{1}(B1)), where w_{1}(B) = w_{0}(B)
= 1 by convention.
Decoding:
• 
Assuming the relay has decoded w_{1}(i1) which was
sent at block i1, it can decode w_{1}(i) by looking for a unique
(i)
such that: 

then based on joint Asymptotic Equipartition Property (AEP),
one has (i)
= w_{1}(i) with probability goes to 1 
• 
The destination decodes from the last block until all blocks are received.
Assuming that it has decode w_{1}(i) in block (i+1), then in block
i, it declare that (i1)
is received, if (u((i1)),
x_{1}(w_{1}(i), (i1)),
y_{2}(i)) are jointly typical. It is easy to see that if:R_{1}<I(U,
X_{1}; Y_{2}) 

(i1)
= w_{1}(i1) with probability goes to 1, as n increases 
• 
Having w_{1}(i1), the destination decodes w_{0}(i) by
looking for a unique (i)
such that (u(w_{1}(i1)), x_{1}(w_{1}(i), w_{1}(i1)),
x_{2}((i),
w_{1}(i1)), y_{2}(i)) are jointly typical. If there does
not exist such unique sequences, the destination occurs an error. Then based
on AEP, the error probability will go to zero if: 
By combining Eq. 1517, the rate pairs
in the closure of the convex hull of all (R_{1}, R_{o}) for
the RCFOM satisfying: R_{1}<min{I(X_{1}; Y_{1}X_{2},
U), I(U, X_{1}, Y_{2})}
for some joint distribution:
p(u, v_{1}, v_{2}, x_{1}, x_{2},
y_{1}, y_{2}) = p(u) p(v_{1}u) p(v_{2}u)
p(x_{1}, x_{2}v_{1}, v_{2}) p(y_{1},
y_{2}x_{1}, x_{2})
are achievable using DF scheme.
Note that if U = X_{2}, Eq. 18 reduces to one of
the main results by Cover and Gamal (1979).
NUMERICAL RESULTS AND ANALYSIS
Here, the achievability results in Eq. 1819
are extended to the Gaussian RCFOM because it approximately presents realistic
wireless networks. The signals received, respectively at the relay and the destination
node are given by:
Table 1: 
The encoding and decoding process for the RCFOM 

Y_{2} = X_{1}+X_{2}+Z_{2} 
(21) 
where, Z_{1}~N(0, N_{1}) and Z_{2}~N(0, N_{2})
are i.i.d gaussian noise. The source and the relay have average power constraints:
and:
If an AWGN RCFOM is said to be degraded, then the relay has all the knowledge
that the destination knows, i.e., the channel inputoutput relations in Eq.
20 and 21 are changed to:
Y_{2} = X_{1}+X_{2}+Z_{1}+Z’ 
(23) 
where, Z_{1}~N(0, N_{1}) and Z’~N(0,
N_{2}N_{1}) are i.i.d gaussian noise for N_{1}<N_{2}.
Let:
denote the capacity function and let:
in the rest of this section. All achievable rate values are expressed in bps
Hz^{1}.
Let U~N (0, P), X’_{1}~N(0,
αP_{1}) and X’_{2}~N(0,
βP_{2}). Also, let:
In the above expressions the parameter β shows the relay’s
participation level in the help of relaying source’s
message which controls the tradeoff between the relayed messages and relay’s
own messages. Although, for the traditional degraded relay channel it is always
optimal to relay source’s message
with full power, this may not be the case when the relay sends its own messages.

Fig. 3: 
The achievable rate regions for the degraded gaussian relay
channel with forwarding own messages 
Therefore, the rate pairs in the closure of the convex hull of all (R_{1},
R_{o}) for the Gaussian relay channel with forwarding own messages satisfying:
are achievable using DF scheme for some α, βε[0, 1].
Note that, set β = 0 and Eq. 26 will reduce to the
capacity of the degraded Gaussian relay channel as another main result by Cover
and Gamal (1979).
Figure 3 illustrates the achievable rate regions to demonstrate
the relationship between the source rate (R_{1}) and the rate of relaying
own messages (R_{o}) for two scenarios for comparison:
• 
Case 1: The degraded gaussian RCFOM with P_{1}
= P_{2} = 10 dB, N_{1} = 2 dB and N_{1} = 4 dB 
• 
Case 2: The nondegraded gaussian RCFOM with P_{1} = P_{2}
= 10 dB, N_{1} = 5 dB and N_{1} = 4 dB 
In the case 2, using the relay performs worse than the case 1 because the system
no longer benefits from using the relay sufficiently to achieve the best achievable
rate when the relay has more noise. Therefore, it is profitable to use the relay
whenever it is more helpful in forwarding the source message to the destination,
i.e., the sourcedestination channel is the degraded version of the sourcerelay
channel.
CONCLUSION
In this study, the relay channel with forwarding own messages was studied.
In particular, the cooperative DF scheme was proposed and the coding strategy
was developed for this channel. Furthermore, upper bounds on the capacity region
and the corresponding achievable performance bounds for this channel were obtained
in discrete memoryless channel and Gaussian channel, respectively. Finally,
numerical results established the critical role of relay’s
own message in the capacity region and shed light on the generalization of this
channel.
This study can be further extended. First, achievable rate regions by using
CF and partial decodeandforward schemes can also be derived in RCFOM. Then,
RCFOM in fading channels is a practical application in wireless networks. Finally,
in order to get greater flexibility of power allocation, global power constraint
instead of a pernode power constraint is worth studying.
ACKNOWLEDGMENTS
This research study is supported by the National Natural Science Foundation
of China (Grant No. 61101125 and Grant No. 61201143).