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
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: email@example.com, firstname.lastname@example.org, email@example.com, firstname.lastname@example.org
Received May, 2013
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
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) . 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.  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  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) . 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
opyright © 2013 SciRes. CN
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
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-
D standing for the distance between the relay
and the destination. Those distances satisfy the condition,
i.e., and .
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 and N
D for the SR, RD and
SD links, and their noise powers are
, 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.
in this paper. Alternatively, the SNR of the
different links are given by
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
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
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.
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.
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
Copyright © 2013 SciRes. CN
Z. TENG ET AL.
denoted as . Here is
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
and expresses energy proportion to symbol node for a
corresponds bit node. The connections between bits and
symbols can also be described by a
Given a bit block , only the bits
with these indices l are sampled by a
modulated symbol, so RPC modulated symbol can be
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
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
UkUk k 1).
Finally, S broadcasts S
to R and D.
3.1. Relay Node Decoding and Compress
Relay node performs RPC decoding, LDPC encoding
and compressing forward in time slot 2. R first receives
Y from S, and
Y is given by
where is noise term of channel SR, and
. Then, R performs RPC decoding, and gets
b is the results of hard decision of original RPC
After decoding, R uses LDPC parity check matrix H to
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.
, 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
N, and can be re-
garded as the side information in DSC. In addition to
information bits, there exist parity bits in
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-
Y from source node S, and
Y can be ex-
Then, D performs RPC decoding algorithms to get soft
informations denoted as ,
bbb bY (9)
Here, we modify the hard decision part of RPC de-
coding algorithm proposed in . Modified RPC decod-
ing algorithm does not estimate the hard decision of input
binary digit, but outputs the probability of corresponding
Figure 3. The diagram of joint decoding.
Copyright © 2013 SciRes. CN
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
Next, D assemble soft information from RPC decoder
and soft parity information from relay node together, we
get input data as following,
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  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
SR RD SD
Figure 4 compares the BER performance in different
schemes. Here “S-D” is the original RPC algorithm,
“”, “R0.89 ”, “R0.94 ” and
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
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
and the sending increasing step in source node
is 10 modulation signals, the SNR range from 5dB to
30dB and :7
. 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
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.
This paper investigates the scheme for parallel concatena-
tion of LDPC and RPC. Though RPC perform the
functionality of coding and modulation simultaneously, its
Copyright © 2013 SciRes. CN
Z. TENG ET AL.
5678910 11 12 1314
S ender S NR(dB)
Rel a y
Rel a y
Rel a y
Rel a y
(a) dSR : dRD = 3 : 7
5678910 11 12 13 14
S end er SNR(dB )
(b) dSR : dRD = 7 : 3
Figure 4. BER performance comparison among different
510 15 20 25 30
Sender SNR (dB)
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-
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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