Distributed Coding Modulation Adaptation Scheme for Relay Channel

doi:10.4236/cn.2013.53B2008

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Communications and Network, 2013, 5, 36-41

http://dx.doi.org/10.4236/cn.2013.53B2008 Published Online September 2013 (http://www.scirp.org/journal/cn)

Distributed Coding Modulation Adaptation Scheme for

Relay Channel

Zi Te ng1,2, Jun Wu1*, Min Wang1,3, Lifeng Su1

1College of Electronics and Information Engineering, Tongji University, Shanghai, China,

2School of Mathematics, Physics & Information Engineering, Jiaxing University, Jiaxing, China,

3School of Mathematics and Computer Science, Gannan Normal University, Ganzhou, China.

Email: 2011tengz@tongji.edu.cn, wujun@tongji.edu.cn, 2011mwangcs@tongji.edu.cn, sulifeng@tongji.edu.cn

Received May, 2013

ABSTRACT

Rate adaptation is an effective approach to achieve high spectrum efficiency under varying channel condition, espe-

cially for wireless communication. This paper proposes rate adaptation at receiver for wireless relay system. In this

scheme, source node uses a new modulation technology, called random projections code (RPC), to achieve rate adapta-

tion. Both relay node and destination node decode the received RPC encoding signals. If destination does not decode

RPC correctly, relay node will act compressing and forwarding role by performing LDPC syndrome encoding and

sending syndrome coded information to destination node. We discuss how to jointly decode at destination node when it

receives RPC coded information from source node and syndrome coded information from relay node. Finally, we

evaluate the scheme by bit-error-rate (BER) and good put evaluation metrics. Simulation results show that the coding

gain is about 4 dB, 3.1 dB, 2.2 dB and 1.6 dB for LDPC coding rate 0.8, 0.89, 0.94, 0.99 at BER 10-5 respectively. The

throughput of the schemes is at least 0.3 bit/s/Hz higher than RPC at SNR ranging from 5 dB to 25 dB.

Keywords: Rate Adaptation; Random Projection Code; LDPC; Relay Channel

1. Introduction

Rate adaptation is critical to the performance of modern

wireless communication system, e.g., WiFi, 3G and LTE.

Conventional rate adaptation technology is implemented

at sending end, and achieved by adjusting actual trans-

mission rate through channel coding rate and modulation

scheme[1,2], based on the current channel state information

(CSI) [3]. However the existing approaches for rate adapta-

tion at sending end have two defects. One is that it is

always difficult to estimate CSI accurately due to feed-

back delay in frequency division duplex (FDD) system,

because the channel may vary drastically during several

data packets transmission. The other is that the trans-

mission rate can be adjusted among limited modulation

coding schemes (MCS), so the coarse granularity of

MCS results in a staircase of spectrum efficiency.

To solve these problems mentioned above, three new

schemes [4-6] have been proposed for smooth rate adap-

tation, and all of them implement rate adaptation at re-

ceiver and attain continuous spectrum efficiency. Cui et

al. [4] has proposed the random projection code (RPC),

which is a novel rate compatible modulation (RCM)

technology, and modulated symbols are incrementally

generated from information bits through weighted map-

ping. Compared to LDPC [7, 8], probability convolution

operation is used in RPC for horizontal iteration instead

of log(tan h) operation. This is due to the fact that RPC

symbols are generated using the arithmetic weighted sum

instead of logical exclusive-OR (XOR). RPC combines

channel coding and modulation together. In addition, Ref-

erence [4] has mentioned that a high coding-rate LDPC

code serially concatenated with RPC can gain better per-

formance, but no detailed performances are given.

On the other hand, how to use RPC in relay channel is

a relative new topic. For traditional relay system, some

researchers have proposed distributed channel coding (DCC)

schemes for the three node relay channel to jointly optimize

coding design at source node and relay node. These DCC

schemes include distributed turbo codes (DTC) and distrib-

uted LDPC codes (DLDPC) [9]. References [10-14] have

discussed how to design LDPC code for DF relay scheme.

If the signal from relay node to destination node is com-

pressed, those DLDPC models can be thought as typical

distributed source coding (DSC). There are two major

kinds of approach, i.e., parity approach and syndrome

approach, to realize DSC [15,16]. Some researchers have

proved that under ideal channel condition syndrome ap-

proach has the optimality, but under the noisy channel

condition parity approach’s performance is the best

[16,17].

Z. TENG ET AL. 37

Inspired by DCC, DSC and potential coding gain

brought by serially concatenating LDPC with RPC, we

propose concatenating LDPC with RPC in parallel, and

apply this parallel concatenation scheme to relay system.

This scheme also has implemented rate adaptation at

receiver with the help of LDPC coding at relay node. To

our knowledge, the parallel concatenation of LDPC and

RPC, and applying it to rate adaptation in relay system

are seldom seen in publication.

The relay system consists of three nodes, i.e., one source,

one relay and one destination. In our scheme, source

node doesn't need CSI, except the ACK signal from des-

tination node. Relay node and destination node achieve

rate adaptation by using RPC. Relay node uses syndrome

encoder to generate syndrome bits which are modulated

by BPSK, and then transmits the modulation symbols to

destination node. In destination node, we adopt joint de-

coder which needs two input data, i.e., the received RPC

encoded information from source node and received

syndrome information from relay node. Compared to

pure RPC scheme, simulation results show that the cod-

ing gain is about 4 dB, 3.1 dB, 2.2 dB and 1.6 dB for

coding rate 0.8, 0.89, 0.94 and 0.99 at BER 10-5, the

proposed schemes can enhance channel capacity at least

0.3 bit/s/Hz at signal-to-noise ratio (SNR) ranging from 5

dB to 25 dB. The simulation also indicates that the gain

is insensitive to distance of relay node to source node and

destination node.

The structure of this paper is organized as follows.

Section 2 gives the system model of our relay scheme.

Section 3 presents the processing procedure of source

node and relay node. Section 4 presents how to decode

jointly at destination node. The simulation results of our

relay schemes are shown in section 5. Finally, Section 6

concludes this paper.

2. System Model

Our system model is depicted as Figure 1. We can see

that this system includes three nodes, i.e., source node

denoted as S, relay node denoted as R, and destination

node denoted as D. There exists three channel links, i.e.,

SD link, SR link and RD link. The distance between the

source and the destination is denoted bySD , SR

standing for the distance between the source and the re-

lay, and

d d

D standing for the distance between the relay

and the destination. Those distances satisfy the condition,

i.e., and .

d

SD SRSD RD

We assume that relay node operates in a half-duplex

mode. AWGN channel model is used for all the links,

denoted as SR ,

d dd

D and N

D for the SR, RD and

SD links, and their noise powers are



, 2



and



, respectively. Setting radio signal propagation at-

tenuation factor as



, the relationships between the

noise powers of different links can be given by

Figure 1. System model of the relay scheme.

and() ()

SR SRRDRD

SD SD





 (1)

Let α2



in this paper. Alternatively, the SNR of the

different links are given by

SR SD

SNR



 (2a)

SR SD

SR SR

SNRSNR d







 



(2b)

1SD

RD SD

RD RD

SNRSNR d







 





(2c)

S uses RPC to encode b, and each two consecutive

symbols are composed one modulation signal denoted as

Then S broadcasts

to R and D. The relay node

R uses RPC decoder2 to demodulate the signal from

source node at first, and gets the information bits denoted

as ˆ

b. Then, R re-encodes ˆ

b by LDPC encoder, and

modulates parity encoded bits by BPSK to generate sig-

nal denoted as

. R transmits

to D. Finally, D

performs a concatenated decoding. After receiving the

signal



from S, D uses RPC decoder1 to de-

modulate signal, and gets the soft information . In the

next time slot, D receives parity encoding information

from relay node, and then D uses as side informa-

tion, performing LDPC decoding. In order to improve

performance, both side information and parity informa-

tion are used in soft information mode.

ˆD

3. Transmitter

This system can be modeled as the time division relay

channel. The total time is divided into three time slots,

i.e., 1, 2, and 3

t, for source node, relay node, and

destination node respectively. In this section, we describe

the detailed process of the source node and relay node.

t t

3.1. Source Encoding and Broadcasting

The encoding principle of RPC is represented by a bipar-

tite graph shown in Figure 2. Cycles denote bits nodes,

and squares denote symbols nodes. A bipartite graph

Z. TENG ET AL.

denoted as . Here is

(,,)GUVE{ },1,...,

Ubj N

Figure 2. The bit-to-symbol mapping graph of RPC.

the set of bits nodes, is the set of

symbols nodes, and E defines the connections between

bit nodes and symbols nodes. A weight corresponding to

an edge belongs to the weight set

{}, 1,...,

Vui M



,,,



www w,

and expresses energy proportion to symbol node for a

corresponds bit node. The connections between bits and

symbols can also be described by a

N mapping

matrix G.

Given a bit block , only the bits

with these indices l are sampled by a

modulated symbol, so RPC modulated symbol can be

written as



,,,

bb bb



1,2,...,il L







 (3)

where L is the number of non-zeros entities in thi



row of G, and l

is signal bits. RPC encodes b into a

series of symbols by

UGb, (4)

where U is the generated symbols block for transmission.

RPC encoding and broadcasting takes place in time

slot 1. After is encoded into U, each two consecu-

tive symbols U are composed as one modulation signal

given by

t S

 

2121,(0,1,,

UkUk k 1).

Finally, S broadcasts S

to R and D.

3.1. Relay Node Decoding and Compress

Forward

Relay node performs RPC decoding, LDPC encoding

and compressing forward in time slot 2. R first receives

signal

Y from S, and

Y is given by

RSS

YXN

(5)

where is noise term of channel SR, and

(0,N



. Then, R performs RPC decoding, and gets

bGF(2 )

ˆargmax{P( |)},





Y (6)

where ˆ

b is the results of hard decision of original RPC

decoding algorithm.

After decoding, R uses LDPC parity check matrix H to

encode ˆ

b again,

H* ,

Pb (7)

where

P is the parity bits. Then, R modulates

with BPSK to form modulation signal

, which is

transmitted to D. Because of only transmitting the parity

bits, R acts as compressing and forwarding role.

4. Jointly Decoding at Destination

In this section, we mainly focus on the joint decoding at

D by using RPC and LDPC. And, we will analysis the

feature of this joint decoding.

4.1. Joint Decoding

The diagram of joint decoding is depicted as Figure 3.

From

axis



, joint decoding at D is divided into two

stages, one is RPC decoding, and the other is LDPC de-

coding. We use the original RPC decoding algorithm in

joint decoding algorithm, but modify the hard decision

part to output soft information as one part of input of

LDPC decoding. The soft information correspond the

information bits nodes from 1

to 1

N, and can be re-

garded as the side information in DSC. In addition to

information bits, there exist parity bits in

axis



, i.e.,

bits node from 11N



to 2N, which corresponds the

channel prior information from relay node, just like

compressing information in DSC.

D performs decoding in two consecutive time slots, i.e.,

2 and . In time slot 2, D receives the signal de-

noted as

t t

Y from source node S, and

Y can be ex-

pressed as





DSS

YXN

(8)

Then, D performs RPC decoding algorithms to get soft

informations denoted as ,

ˆD

(2 )

ˆˆˆ

(, )argmax{P(|)}

bGF



DDD SD

bbb bY (9)

Here, we modify the hard decision part of RPC de-

coding algorithm proposed in [4]. Modified RPC decod-

ing algorithm does not estimate the hard decision of input

binary digit, but outputs the probability of corresponding

bits.

Figure 3. The diagram of joint decoding.

Z. TENG ET AL. 39

In time slot 3, after D received signal from relay

node, D performs LDPC decoding. D receives the signal

Y from R, and

Y can be presented by

DRS

YXN









(10)

Next, D assemble soft information from RPC decoder

and soft parity information from relay node together, we

get input data as following,

 

and

1,0,

0, 0,

ji ji

QbYQb

 



 

 



(11)

where

, and

2()/

() 1

1RD RD

YiY Y

e







)

(12)

4.2. Analysis

The scheme proposed in this paper has two important

features. The first is that it realizes the rate adaptation at

receiver. Due to using RPC decoding at relay node and

destination node, our system will automatically decode

the signal from source node according to the channel

quality. As long as source node does not receive the

ACK from destination node, it will keep broadcasting

more and more modulation symbols to relay and destina-

tion node. With the increase of receiving symbols, the

probability of RPC decoding success will improved.

Otherwise, source node will send next data frame. With

the help of LDPC encoding at relay node, the joint de-

coding performance in destination node is significantly

improved. Thus, the number of demodulation symbols

for RPC decoding can be dramatically reduced. In an-

other words, joint decoding can decode successfully with

much less symbols from source node with the help of

relay. The second one is that joint decoding at destination

node has two parts input, i.e., parity information from

relay node and soft information from RPC encoder2. The

joint decoding performance will be improved with the

improvement of reliability of input data. Obviously, the

reliability of soft information and parity information are

improved with the help of relay node.

5. Simulation Results

In this section, we implement the decoding algorithm of

RPC and LDPC algorithm, and use them to construct a

relay system discussed in Section II. In our experiment,

we select the SNR in SD link from 5dB to 30dB, and

think as usual the SNR in SR link and RD link are all

better than SD link. Here we consider a special case in

relay model where the distance proportion of relay node

to source node, relay node to destination node and source

node to destination node is 7:3:1 and

3:7:1. In addition we experiment the bits block size is

and the numbers of parity bits generated in

relay node is 100, 50, 25 and 10 corresponding to the

different LDPC coding rate 0.8, 0.89, 0.94 and 0.99

respectively. Finally, we use goodput [18] and BER as

evaluation metrics to evaluate the performance of our

scheme. No matter what kinds of evaluation metric, we

all assume that ACK is immediately available in our

simulation.

(: :

SR RD SD

ddd

400N

Figure 4 compares the BER performance in different

schemes. Here “S-D” is the original RPC algorithm,

“”, “R0.89 ”, “R0.94 ” and

“R0.99

Re ” is our scheme with different LDPC coding

rate in relay node. From Figure 4, we can see that all

these relay schemes are better than “S-D”. And with the

LDPC coding rate dropping the performance of our

scheme is better and better. For example, as shown in

Figure 4(a), when SR RD and BER equal 10-5,

our relay schemes have performance improved about

4dB, 3.1dB，2.2dB and 1.6dB more than “S-D”. In ad-

dition, we can find that there are the similar perform-

ances when SR RD

R0.8

Relay

lay 

Relay

:dd

:7:3

Relay 



as shown in Figure 4(b).

The main reason is that it is usually thought that the

communication condition in SR link and RD link are all

better than SD link, so the RPC decoding performance in

relay node is better than destination node, which makes

the correctness of RPC decoding in relay node all im-

proved and the reliability of the parity bits similar in des-

tination too. Thus, with the help of relay node, the whole

system performance is less relation with the relay node’s

location when the LDPC rate in relay node is the same.

We also evaluate our scheme by good put metric in the

actual wireless scenario. Here we set the bits block size is

400N



and the sending increasing step in source node

is 10 modulation signals, the SNR range from 5dB to

30dB and :7

SR RD

dd :3



. In order to test the perform-

ance of our scheme, we also consider the LDPC rate with

0.8 and 0.94. Figure 5 shows the result where “S-D” is

the original system without relay, and “R0.8

Re ” and

“R0.94

Re ” are our scheme. We can observe that our

different schemes are all higher than “S-D” at least 0.38

bit/s/Hz and 0.28 bit/s/Hz when SNR from 5dB to 25dB.

But all the throughputs are almost the same value 6.6

bit/s/Hz when SNR more than 25dB.Obviously, the rea-

son we can achieve higher throughput is the relay’s help.

In addition, we also can observe that with the increasing

of the LDPC rate, the goodput became higher and higher.

The main reason is that the LDPC rate higher can pro-

vide more protection to information bits.

lay

lay 

6. Conclusions

This paper investigates the scheme for parallel concatena-

tion of LDPC and RPC. Though RPC perform the

functionality of coding and modulation simultaneously, its

Z. TENG ET AL.

5678910 11 12 1314

-6

-5

-4

-3

-2

-1

S ender S NR(dB)

BER

Rel a y

R=0.8

Rel a y

R=0.89

Rel a y

R=0.94

Rel a y

R=0.99

S-D

(a) dSR : dRD = 3 : 7

5678910 11 12 13 14

10-6

10-5

10-4

10-3

10-2

10-1

S end er SNR(dB )

BER

Rel ay

R=0.8

Rel ay

R=0.89

Rel ay

R=0.94

Rel ay

R=0.99

S-D

(b) dSR : dRD = 7 : 3

Figure 4. BER performance comparison among different

schemes.

510 15 20 25 30

Sender SNR (dB)

Goodput (bit/s/Hz)

Rel ay

R=0.8

Realy

R=0.94

S-D

Figure 5. Throughputs co mparison of SD link and different

relay channel schemes.

coding performance is not good enough. As we expect,

the concatenation of LDPC and RPC brings significant

gain, e.g., coding gain 4 dB, 3.1 dB，2.2 dB and 1.6 dB

for coding rate 0.8, 0.89, 0.94 and 0.99 respectively.

On the other hand, parallel concatenation structure fits

the 3-node relay system well. In order to reduce overhead,

we make use of distributed source code concept here, and

relay node only sends parity code bits. The destination

node uses the direct-link signal as side information, and

relay-link signal to perform joint decoding. This scheme

further improves rate adaptation feature of RPC. The

efficient improvement of 0.3 bit/s/Hz spectrum is ob-

tained. Next step, we plan to investigate the joint code

design of RPC and LDPC to optimize performance fur-

ther.

7. Acknowledgements

The author wishes to thank the reviewers for their con-

structive comments which greatly improve the presenta-

tion of these results. This work is financially supported

by NSFC General Program under contract No. 61173041.

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