Application of Rate Compatible Punctured Turbo Coded Hybrid ARQ to MC-CDMA
Mobile Radio
Deepshikha GARG† and Fumiyuki ADACHI‡
Department of Electrical and Communication Engineering, Tohoku University
Aza-Aoba 05, Aramaki, Aoba-ku, Sendai, 980-8579 Japan
E-mail: †deep@mobile.ecei.tohoku.ac.jp, ‡adachi@ecei.tohoku.ac.jp
Abstract MC-CDMA, a multicarrier modulation scheme basedon code division multiple access (CDMA) is the most likely
candidate for the next generation of mobile radio
communications. Rate compatible punctured turbo coded hybrid
ARQ (RCPT HARQ) has been found to give improved
throughput performance in a DS-CDMA system. In this paper,
we apply RCPT HARQ to an MC-CDMA system and evaluate bycomputer simulations the throughput performance of the RCPTHARQ in a frequency selective Rayleigh fading channel. It was
found that the throughput performance of RCPT HARQ is almost
insensitive to channel characteristics. The performance can be
drastically improved with receive diversity combined with spacetime transmit diversity (STTD). In addition, the comparison of
RCPT HARQ in MC-CDMA, OFDM and DS-CDMA systems
shows that, under similar conditions, the throughput in MCCDMA is the best over a frequency-selective fading channel.

I. INTRODUCTION
In broadband mobile radio communications, thetransmitted signal is scattered by many obstacles locatedbetween a transmitter and a receiver, thereby creating a
propagation channel with numerous paths having different
time delays. The transfer function of such a broadband
channel is no more constant over the signal bandwidth andis referred to as the frequency-selective fading channel [1].
For successful communications in such fading channels,
some powerful multi-access schemes and error control
techniques are necessary.
Recently, a new CDMA system based on the
combination of CDMA and multicarrier (MC) modulation
based on orthogonal frequency division multiplexing(OFDM), called MC-CDMA, has been attracting muchattention [2] and is under extensive study. In MC-CDMA,each user’s data-modulated symbol to be transmitted isspread over a number of subcarriers using an orthogonal
spreading sequence defined in the frequency-domain.
One of the most powerful error control techniques ishybrid ARQ (HARQ) with turbo codes. Turbo codes [3],introduced in 1993 by Berrou et al., have been intensively
studied as the error correction code for mobile radio
applications. In [4], it is shown that in a DS-CDMAsystem, the throughput of type II RCPT HARQ scheme
outperforms other ARQ schemes over fading andshadowing channels. The performance analysis of RCPTHARQ in DS-CDMA system in a frequency-selective
fading channel can be found in [5] and is shown that thebest performance is attained by type II RCPT HARQ whenminimum amount of redundancy bits is transmitted witheach retransmission. RCPT HARQ performance in an
OFDM system has been examined in [6]. However, theextent to which the RCPT HARQ improves the throughput
performance in a MC-CDMA mobile radio has not been
fully understood. In this paper, we apply RCPT HARQ to
MC-CDMA system and evaluate by computer simulations

the performance of the RCPT HARQ in an MC-CDMAsystem over a frequency-selective Rayleigh fading channel.
The improvement in throughput performance attainable in
an MC-CDMA system with transmit and receive diversity
is also evaluated and is compared with those in OFDM and
DS-CDMA systems.
The remainder of this paper is organized as follows.
Section 2 reviews the RCPT HARQ scheme considered inthis paper. The transmission system model using MCCDMA is presented in Section 3. In Section 4, we present
and discuss the effect of various system and propagation
parameters on the throughput performance of RCPTHARQ in MC-CDMA and compare it with those in DSCDMA and OFDM. Section 5 offers some conclusions.

REVIEW ON RCPT HARQ SCHEMES [5~6]II.

The various hybrid ARQ schemes considered in thispaper are obtained from the rate 1/3 turbo code bypuncturing it with different puncturing period P. The turbo
encoder/decoder parameters are shown in Table 1. A rate
1/3 turbo encoder, fed with an information bit sequence oflength N, produces a systematic bit sequence (information
bit sequence) of length N and 2 parity bit sequences, eachof length N. The 3 sequences are punctured according to apuncturing pattern represented by a 3 × P matrix.
In type I scheme, the two parity bit sequences are
punctured according to the P=2 puncturing matrix
ª1
«1
«
«¬ 0

1º
0 »»
1 »¼

and transmitted along with the systematic bit sequence. If
the receiver detects errors in the decoded sequence, aretransmission of that packet is requested. The
retransmitted packet uses the same puncturing matrix as
the previous packet.
In type II HARQ, we consider three schemes
represented by S-Px (systematic-puncture period of P=x)with x=2, 4, and 8. The puncturing matrices for the firsttransmission to (x+1)th transmission are as follows:
Puncturing matrices for S-P2 (binary notation):ª1 1 º»««0 0 »«¬0 0»¼ª0 0 º»««1 0 »«¬0 1»¼ª0 0 º»««0 1 »«¬1 0»¼

Puncturing matrices for S-P4 (binary notation):
ª1
«0
«
«¬ 0

1

1

0
0

0
0

1º
0 »»
0 »¼

ª0
«1
«
«¬ 0

0

0

0
0

0
1

0º
0 »»
0 »¼

ª0
«0
«
«¬ 0

0

0

1
0

0
0

0º
0 »»
1 »¼

ª0
«0
«
«¬ 1

0

0

0
0

1
0

0º
0 »»
0 »¼

ª0
«0
«
«¬ 0

Puncturing matrices for S-P8 (octal notation):ª3 7 7 º»««0 0 0»«0 0 0»»¼¬«ª0 0 0º»««0 1 0»« 2 0 0»¼»¬«

1

ª0 0 0º»«« 2 0 0»«0 1 0»»¼¬«ª0 0 0º»««1 0 0»« 0 0 4»¼»¬«

ª0 0 0º»««0 0 2»«0 4 0»»¼¬«ª0 0 0º»««0 0 1 »«0 2 0»¼»¬«ª0 0 0º»««0 2 0»«0 0 1»»¼¬«ª0 0 0º»««0 4 0»«0 0 2»¼»¬«ª0 0 0º»««0 0 4»«1 0 0 »
»¼
¬«

0

0

0
1

0
0

0º
1 »»
0 »¼

The first transmission consists of transmitting only
the systematic bit sequence. The number of bits
transmitted in the second transmission onwards differs
depending on the puncturing period and is 2N/x. As thenumber of retransmissions increases, the resultant code
rate decreases. After each retransmission, turbo decoding
is performed at the receiver. Presence of errors even afterthe (x+1)th transmission causes the sequences ofsystematic bits and punctured parity bits to be transmitted
again in the subsequent transmissions. In all the schemes
incremental redundancy and packet combing are utilized.

Type II HARQ S-Px

K

K

Information {uk }1st Tx.

Rate 1/3
turbo encoder
Systematic {uk }…

2nd Tx.

…

3rd Tx.

…

4th Tx.

…

(x+1)th Tx.

(1)Parity1 { pk }(2)

Parity2 { pk }

K

2K/x

Table 1: Turbo encoder/decoder parameters
Rate
1/3
Encoder
Component encoder(13, 15) RSC
Interleaver
S-random (S=K1/2)
Component decoder
Log-MAP
DecoderNumber of iterations 8

Type I HA RQ
2KKFigure 1. Different HARQ schemes.

MC-CDMA signal received on each antenna isdecomposed into the Nc orthogonal subcarrier components
by applying the FFT. The frequency-domain minimum
mean square error (MMSE) equalization based on thesubcarrier-by-subcarrier error minimization is carried out[7] and multiplied by the common PN-code. The Nc
subcarrier components are then despread using thedifferent othrogonal codes. For each code, Nc/SF symbols
are obtained; a total of Nc symbols are received per MCCDMA signaling interval. After parallel-to-serial (P/S)
conversion, the soft decision sample sequence is deinterleaved and input to the RCPT decoder which consistsof a de-puncturer, a buffer and a turbo-decoder. Error
detection is performed by the CRC decoder which
generates the ACK/NAK command and recovers theinformation sequence in case of no errors.
When space-time transmit diversity (STTD) [8] isapplied, 2Nc symbols are transmitted over two MC-CDMAsignaling intervals from the two transmit antennas. At theIII. TRANSMISSION SYSTEM MODEL
The transmission system model is shown in Fig. 2.
At the transmitter, a CRC coded sequence is input to the
RCPT encoder where it is turbo coded, punctured andstored in the buffer for possible retransmissions. The
punctured sequences, which are of different length fordifferent puncturing periods, are block-interleaved anddata-modulated. The data-modulated symbol sequence isserial-to-parallel (S/P) converted to Nc symbol streams.
Each symbol in the Nc streams are copied SF times andmultiplied by an orthogonal code. The SF code multiplied
symbols are then added, multiplied by a long common
pseudo-noise (PN) sequence and transmitted over the Nc
subcarriers. This is done by applying the inverse fast
Fourier transform (IFFT). After the insertion of a guardinterval (GI), the MC-CDMA signal is transmitted
over afrequency- selective Rayleigh fading channel
and is received by multiple antennas at the receiver. The

Code #SF-1

P/S Conversion

N c point IFFT

Copier
Copier…

S/P Conversion

Data
Modulator

Interleaver

Tx. Buffer

Puncturer

Turbo Encoderpn( N c − 1)……

……

c 0 ( SF − 1)+GItransmitted
MC-CDMAsignal…

c (0 )

0…

CRC Encoder…

ACK/NA K

c 0 ( SF − 1)

…

S/P

...

Binary
data

pn(0)
…

c 0 (0)Code #0
RCPT Encoder(from receiver)(a) Transmitterc 0∗ (0)…

Channel Est./Wt. Comp.
(b) Receiver

Figure 2. Transmission system model.

2

Rx.Buffer
DePuncturer

Turbo
Decoder

CRC Decoder

De-interleaver

P/S

De-modulator¦

RCPT Decoder…

…

c 0∗ ( SF − 1)¦…

c 0∗ (0)…

Nc point FFT…

…

S/P Conversion…

c 0∗ ( SF − 1)

Code #0

P/S Conversion…

…

received-GI
MC-CDMAsignalCode #SF-1…

pn ∗ (0)ACK/NA K

Info. Est.

receiver, frequency-domain MMSE equalization is jointly
performed with STTD decoding [9].
IV. SIMULATION RESULTS
The turbo encoder/decoder parameters are as shownin Table 1. The computer simulation conditions are
summarized in Table 2.
The information sequence length K=1024bits (Krepresents the CRC encoded sequence length) is assumed
unless otherwise stated. The turbo encoded sequence isinterleaved with a size 2a x 2b block-interleaver, where aand b are the maximum allowable integers for a given
sequence size and are determined so that an interleaver as
close as possible to a square interleaver can be obtained.
Coherent BPSK modulation and ideal channel estimation
are assumed for data demodulation at the receiver. It is
assumed that the number of multiplexed codes is the sameas SF, and SF=256 unless otherwise stated. The fading
channel is an L=16-path Rayleigh fading channel with an
exponential power delay profile having a decay factor α
and the propagation time delay difference of ∆T between
the nearest two paths. When α=0, the power delay profile
is uniform having a normalized delay spread ofτrms/Ts=0.036. For ARQ, an error-free reverse channel andideal error detection are assumed. The number ofretransmissions is taken to be infinite. Throughput
efficiency η is defined as the ratio of bits transmitted
successfully to the total number of bits transmitted [10].
TABLE 2: Simulation Conditions
Information
sequence length
Channelinterleaver
Modulation/
demodulation

MC-CDMA

ARQ
Propagation
channel

K=210 ~ 214 bits
Block interleaver
Coherent BPSK
No. of subcarriers
Subcarrier
spacing
Guard interval
Spreading factor
Type
Max. no. of tx.
Forward
ReverseNc=256
1/Ts
Tg=8/Ts
SF=1~256
Basic, Type I, Type II∞
L=16-path Rayleigh fading
fDT= 0.001
Ideal

A. Comparison of various HARQ schemes
Figures 3 and 4 plot the average number oftransmissions and throughput as a function of the signal
energy per coded bit-to-AWGN power spectrum density
ratio Ec/N0 with the puncturing period P as a parameter for
α=∞dB (single path) and α=0dB (uniform profile). For
reference, the average number of transmissions and thethroughput for basic ARQ (where channel coding is notapplied) are also plotted.
The existence of multiple paths tends to cause thechannel gains of the different subcarriers to vary
independently. This results in frequency diversity, but at
the same time orthogonality among the spreading codes ispartially destroyed. MMSE equalization can restore theorthogonality to a certain extent. We see from Fig. 3 thatwhen α changes from ∞dB to 0dB, the increase in the
average number of transmissions is drastic when channel

coding is not applied due to the increase in random errors
owing to the channel selectivity. However the average
number of transmissions changes only slightly when RCPTHARQ is applied as turbo codes are better suited to correct
random errors. Among the RCPT HARQ schemes, the best
throughput is attained with type II S-P8 as minimum
amount of parity bits is transmitted with eachretransmission. Since the type II S-P8 scheme was foundto give the best throughput performance, it has been used
to evaluate the impact of other system and propagation
parameters.
B. Impact of information sequence length
It is well known [3] that the turbo coding gain
depends on the information sequence length (K). The
longer the information sequence length, the better is the bit
error rate (BER) performance as the internal interleaver
size becomes larger and the allowable size of channel bit
interleaver also becomes larger. In the original paper onturbo coding by Berrou et al. [3], and many of thesubsequent papers, impressive results on the BER
performance have been presented for coding with verylarge information sequence lengths of the order of 65536
bits. On the other hand, since the probability of frame error
can be generally reduced according to the decrease intransmitted sequence length, ARQ schemes are better
suited for shorter information sequence length. The
throughput vs. information sequence length is plotted inFig. 5 for various average received Ec/N0 values. It is seenthat the throughput is almost independent of theinformation sequence length.
C. Impact of spreading factor
In MC-CDMA, when the number C of multiplexed
codes is the same as SF, the data rate remains constant andis the same as in OFDM, which can be seen as a special
case of MC-CDMA with SF=1. With SF=Nc, each symbolis spread over the entire subcarriers available, while eachsymbol is mapped onto a different subcarrier when SF=1.
Figure 6 plots the throughput for type II S-P8 scheme as afunction of average received Ec/N0 with SF as a parameter
for C=SF. It is seen that for lower average received Ec/N0,
the throughput is almost independent of SF. However, forhigher Ec/N0, the throughput increases with the increase in
SF. A 20% increase in throughput is seen for SF=256
compared to SF=1 when Ec/N0=20dB. This is because of
the large frequency diversity effect that can be obtained
when each data symbol is spread over all subcarriers.
D. Impact of channel delay spread
The delay spread is related to the decay factor α.
Figure 7 plots the throughput as a function of the delay
spread expressed in terms of τrms/Ts. As τrms/Ts increases,
the frequency-selectivity of the channel becomes stronger.
When SF=256, each symbol is spread over the entire
subcarriers available; the fading experienced by all thesymbols in an MC-CDMA signaling interval is the same.
However, when SF<Nc, the fading differs for the symbols
in an MC-CDMA signaling interval. This results in more
random errors as τrms/Ts increases. Hence, the throughput

3

E. Impact of antenna diversity
So far, we have considered the single antenna
reception case. Recently, using multiple transmit/receive
antennas has been looked upon as a desirable technique toimprove throughput, i.e., the data rate. We consider STTD
with two transmit antennas and M-antenna receive
diversity. Figure 8 plots the effect of using multiple
antennas at the transmitter and receiver. The throughput
with single transmit and single receive antenna is 0.72 at
the average received Ec/N0=6dB. Using two antennas at thereceiver improves the throughput by about 14%. Using
STTD with antenna diversity reception can further
improve the performance by about 10% at Ec/N0=6dB.
Total improvement with STTD and two antenna receive
diversity is about 25% compared to that of no diversity.
This shows that RCPT HARQ is effective in the presenceof STTD and receive antenna diversity as well.
F. Throughput comparison in MC-CDMA, OFDM and
DS-CDMA
The throughput performances of RCPT HARQ in
MC-CDMA, OFDM and multicode DS-CDMA are
compared here. 2-transmit antennas (for STTD) and 2receive antennas are assumed. For a fair comparison, we
take the number Nc of subcarriers in OFDM to be the sameas in MC-CDMA. In addition, the spreading factor SF in
DS-CDMA is assumed to be the same as that in MCCDMA, i.e. SF=256. A SF-multicode DS-CDMA system
is considered so as to get a data rate equal to that in the
MC-CDMA system (note that the transmission bandwidthof OFDM / MC-CDMA system is 9/8 times wider thanthat of multicode DS-CDMA system). Figure 9 plots thethroughputs of RCPT HARQ in MC-CDMA, OFDM and
DS-CDMA. Time delay separation between consecutive
paths is 1 FFT sample for MC-CDMA/OFDM system and1 spreading chip for DS-CDMA system. Ideal coherent
rake receiver is assumed for the DS-CDMA system. It isseen that for α=∞dB (single path), the throughput in MCCDMA/OFDM system has a slightly lower throughput
than in DS-CDMA because of the power penalty of guardinterval insertion. For α=0dB (uniform profile), thethroughput performance degrades in both OFDM and DSCDMA, but, it remains unchanged in MC-CDMA. The
existence of multiple paths distorts the orthogonality
among the time domain spreading codes and this produces
large inter-code interference. Hence, the throughput
performance in multicode DS-CDMA is severely affected.
The frequency-selectivity also affects the OFDM system aspacket errors increase with the increase in frequencyselectivity. However, the MC-CDMA system is notaffected because of frequency-domain MMSE equalization.

selectivity when each symbol is spread over all thesubcarriers available; spreading each symbol over all thesubcarriers gives the highest throughput. It was also foundthat the throughput is almost independent of theinformation sequence length. The performance can be
improved by 25% when receive diversity is used together
with STTD compared to the single transmit and single
receive antenna case. In addition, the comparison of RCPTHARQ in MC-CDMA, OFDM and DS-CDMA shows that,
under similar conditions, the throughput in MC-CDMA is
the best in a frequency-selective fading channel.
REFERENCES[1]

W. C., Jakes Jr., Ed., Microwave mobile communications, Wiley,
New York, 1974.
[2] S. Hara and R. Prasad, “Overview of multicarrier CDMA,” IEEE
Commun. Mag., pp.126-144, Dec. 1997.
[3] C. Berrou, A. Glavieux, and P. Thitimajshima, “Near Shannon limit
error-correcting coding and decoding - Turbo codes,” Proc. Int.
Conf. Communications, pp. 1064-1070, May 1993.
[4] T. Ji and W. E. Stark, “Turbo-coded ARQ schemes for DS-CDMAdata networks over fading and shadowing channels: throughput,
delay and energy efficiency,” IEEE Journal on Select. Areas inCommun., Vol. 18, pp. 1355-1364, Aug. 2000.
[5] D. Garg, and F. Adachi, “Throughput of RCPT Hybrid ARQ for
DS-CDMA with Diversity Reception and Rake Combining,” Proc.
of IEEE VTC03 Spring, pp. 2730-2734, Korea, April 2003.
[6] D. Garg and F. Adachi, “Rate compatible punctured turbo-codedhybrid ARQ for OFDM in a frequency selective fading channel,”Proc. of IEEE VTC03 Spring, pp. 2725-2729, Korea, April 2003.
[7] F. Adachi and T. Sao, “Joint antenna diversity and frequencydomain equalization for multi-rate MC-CDMA,” IEICE Trans.
Commun., Vol. E86-B, Nov. 2003, to appear.
[8] S. Alamouti, “A simple transmit diversity technique for wirelesscommunications”, IEEE Journal on Select. Areas in Commun., Vol.
16, No. 8, pp. 1451-1458, Oct. 1998.
[9] D. Garg and F. Adachi, “Joint space-time transmit diversity andminimum mean square error combining equalization for MCCDMA”, Technical Report of IEICE, CS2003-41, pp. 79-84,
Yonezawa, Japan, June. 2003.
[10] J. Hagenauer, “Rate-compatible punctured convolutional codes(RCPC codes) and their application”, IEEE Trans. Commun., Vol.
36, pp.389-400, April 1988.
10

M=1, fDT=0.001

no codingtype I
S-P2
S-P4 type II
S-P8

8

s
no
ssi
i
m
s
na
rt
of
er
b
m
u
n
ge
ar
ve
A

Average number of transmissions

which is prone to random errors, decreases for SF=16 and1 as the delay spread increases.

6

α=0dB
α
=0dB
α=∞dB
α
=∞dB
4

2

V. CONCLUSION
In this paper, RCPT HARQ was applied to MCCDMA. It was found that when channel coding is not used,
the throughput decreases with the increase in channel
frequency-selectivity, however, for type II S-P8, thethroughput is almost insensitive to channel frequency-

0
0

5

10

15

20

25

30

Average received Ec/N0 [dB]

Figure 3. Average no. of transmissions of various HARQ schemes.

4

1

1

M=1, fDT=0.001
20dB
0.8
0.8

Throughput

Throughput

10dB

t 0.6
u
p
hg
u
or
h
T 0.4

t
pu
h
g 0.6
u
or
h
T

α=0dB
α=∞dB

Average received E c/N0 =0dB

no codingtype I
S-P2
S-P4 type II
S-P8

0.2

0.4

SF=1
Type II S-P8
M=1, fDT=0.001

SF=16
SF=256

0

0.2

0

5

10

15

20

25

30

0

0.01

c

0.02

0.03

0.04

τ /T

Average received E /N [dB]0

rms

Figure 7. Impact of channel delay spread τrms/T.

Figure 4. Comparison of various HARQ schemes.
1

1

20dB

Type II S-P8
f T=0.001

16dB

D

0.9

12dB
0.8

8dB

Throughput

Throughput

0.8

4dB

0.6

0.7

0.6

0.4

Average received Ec/N0=0dB

Tx. ant =1, Rx. ant =1
Tx. ant =1, Rx. ant =2
Tx. ant =2, Rx. ant =1
Tx. ant =2, Rx. ant =20.5

M=1, f T=0.001
D

Type II S-P8
0.2

10

2048

12
4096

6144

13
8192

0.4

14 4
4
4
4
1.024 10 1.229 10 1.434 10 1.638 10

0

Information sequence length (log 2K)

5

10

15

20

Average received E /N per rx. antenna [dB]cFigure 5. Impact of information sequence length.

0

Figure 8. Impact of antenna diversity.

1

1

Tx. ant. =2, Rx. ant. =2
Type II S-P8
fDT=0.001

M=1, f T=0.001
D

Type II S-P8

0.9

0.9

ut
p
h
g
0.8
u
or
h
T

Throughput

Throughput

0.8

0.7

0.6

C=SF
SF=256
SF=64
SF=16
SF=4
SF=1

0.5

α=0dB
α=∞dB

0.7

DS-CDMA
OFDM
MC-CDMA

0.4
0

5

10

15

0.6

20

0

Average received E /N [dB]
c

0

5

10

15

20

Average received E /N per rx. antenna [dB]cFigure 6. Impact of spreading factor for C=SF.

0

Figure 9. Throughput comparison in MC-CDMA, OFDM and DSCDMA.

5