RCPT hybrid ARQ with limited number ofretransmissions in DS-CDMA mobile radio
D. Garg, R. Kimura and F. Adachi
The effect of a limited number of retransmissions is investigated for
RCPT coded type I and II hybrid ARQ schemes in a DS-CDMA
mobile radio. It is found by computer simulations that the type IIscheme with minimum amount of parity bits transmitted in eachretransmission gives the highest throughput. However if the signal
energy is to be kept lowest, the best scheme depends on the maximum
number of transmissions allowed: the type I scheme is the best fordelay sensitive real-time applications and type II is suitable for delay
tolerant applications like packet data communications.

Introduction: The rate compatible punctured turbo (RCPT) codedhybrid ARQ scheme has been shown to achieve enhanced throughput
performance over an additive white Gaussian noise (AWGN) channel[1] and over fading and shadowing channels [2]. If the allowable
number of transmissions is unlimited, the retransmissions continue
until an error-free information sequence is recovered at the receiver.
However in a practical system, the number of retransmissions allowed
is limited to avoid unacceptable time delay before the successfultransmission of a packet. When the number of allowable transmissions is limited to Imax, error-free reception is not guaranteed andresidual error results. The average number of retransmissions (hencethe additional redundancy bits transmitted) differs for different valueof Imax even if the average received signal energy per coded
bit-to-additive white Gaussian noise (AWGN) power spectrum density
ratio, Ec=N0, is the same. This causes the average required signal
energy per information bit-to-AWGN power spectrum density ratio,
Eb=N0, defined as Eb=N0 ¼ (Ec=N0)=Z, to change as Imax changes, forthe given residual bit error rate (BER). Here, Z is the throughput
defined as Z ¼ N=Ntotal, where N and Ntotal are the number of
information bits and total number of bits transmitted, respectively.
In this Letter, we consider type I and II RCPT coded hybrid ARQ
schemes for a direct sequence code division multiple access(DS-CDMA) mobile radio. We evaluate by means of computer
simulations the effect of a limited number of retransmissions on thethroughput and the required Eb=N0 to find which hybrid ARQ scheme
maximises the throughput and minimises the required Eb=N0.

RCPT coded hybrid ARQ: The various hybrid ARQ schemes
considered in this Letter are obtained from the rate 1=3 turbo codeby puncturing it with different puncturing period P. A rate 1=3 turbo
encoder produces a systematic bit sequence (information bitsequence) of length N and two parity bit sequences, each of length
N. The three sequences are punctured according to a puncturing
pattern represented by a 3  P matrix. In the type I scheme, twoparity bit sequences are punctured according to the puncturing matrix
with P ¼ 2:231 141 05
0 1Fig. 1 Throughput for residual BER ¼ 104Fig. 2 Required signal energy per information bit for residual BER ¼ 104and transmitted along with the systematic bit sequence. If the receiver
detects errors in the decoded sequence, a retransmission of that packet
is requested. The retransmitted packet uses the same puncturing matrix
as the previous packet. In type II hybrid ARQ, we consider threeschemes represented by S-PP (systematic-puncture period of P) withP ¼ 2, 4, and 8. The puncturing matrices for the first transmission to(P þ 1)th transmission are as follows:
23 23 231 10 00 0
4 0 0 5 4 1 0 5 4 0 1 5 for S-P20 00 1
1 03201 1 1 176
64 0 0 0 0 54 1
00 0 0 0
32
200 0 0 0
76
64 0 0 1 0 54 00
1 0 0 0223640020640
1206400332
0 0 0 00 0 0776
0 0 0 54 0 1 0 0 50 0 0 10 1 030 0 0
70 0 1 5 for S-P41 0 032323200 0 00 0 07 7767676
0 0 54 2 0 0 54 0 0 2 54 000 4 00 1 00 03232
3200 0 00 0 00 07676
760 4 54 0 1 0 54 1 0 0 54 000 0 42 0 00 0
30 0
74 0 5 for S-P8 (in octal notation)
0 2

30 0
72 050 130 0
70 152 0

The first transmission consists of transmitting only the systematic bitsequence. The number of bits transmitted in the second transmission
onwards differs depending on the puncturing period and is 2N=P. As thenumber of retransmissions increases, the resultant code rate decreases.
After each retransmission, turbo decoding is performed at the receiver.
Presence of errors even after the (P þ 1)th transmission causes thesequences of systematic bits, and punctured parity bits to be transmitted
again in the subsequent transmissions.

Computer simulation: In this Letter, the single user case is considered (or the other user interference is approximated as a Gaussian
noise and thus combined with the AWGN). The information bit length
N ¼ 1024 is assumed. The RCPT coded sequence to be transmitted isblock-interleaved by a channel interleaver and then transformed into
binary phase shift keying (BPSK) data symbol sequence. For channel
estimation, four known pilot symbols are time-multiplexed every 32
data symbols. Spreading is implemented by multiplying the pilotinserted BPSK sequence with the long pseudorandom (PN) chipsequence. Spreading factor (SF) is taken to be 32. The spreadsignal is transmitted via a 4-path Rayleigh fading propagation channelwith uniform power delay profile and normalised maximum Doppler
frequency fDTc ¼ 3.1  105, where Tc is the chip interval of spread-

ELECTRONICS LETTERS 23rd January 2003 Vol. 39 No. 2

ing sequence. The receiver has a 4-finger coherent RAKE combiner,
in which channel estimation is performed based on the pilot symbol
assisted K ¼ 2 WMSA channel estimation [3]. After BPSK demodulation the soft decision sample sequence is de-interleaved and RCPT
decoded using log-MAP algorithm. A retransmission is requested iferrors are detected. An error-free reverse channel and perfect error
detection are assumed throughout the Letter.
We first discuss the throughput performance and then the required
Eb=N0. Fig. 1 shows the throughput Z for the different hybrid ARQ
schemes against Imax for a residual BER of 104. It can be seen in theFigure that the type I scheme has the lowest throughput followed by thetype II S-P2, S-P4 and S-P8 schemes. S-P8 scheme has the highest
throughput at all times as the redundancy bits transmitted with eachretransmission is the least. The required Eb=N0 ( ¼ (Ec=N0)=Z) is
computed from the knowledge of residual BER and throughput. First,the Ec=N0 needed for the required residual BER is found and Z for that
Ec=N0 is obtained. The values of Eb=N0 are then calculated and shownin Fig. 2 against Imax for a residual BER of 104. It can be seen that foreach hybrid ARQ scheme, there exists an optimum Imax that attains aminimum Eb=N0. The reason for this is explained below. The increasein Imax reduces the residual BER and thus, decreases the required
average Ec=N0 causing the Eb=N0 to reduce. However if Imax is toolarge, a slow decrease in the required average Ec=N0 is approached,while the average number of redundancy bits increases causing theEb=N0 to increase. For delay sensitive systems, e.g. packet voicecommunications, Imax  2 may be required and hence, the type I
hybrid ARQ scheme is the most favourable as it requires the minimum
Eb=N0. For packet data transmissions, the delay is not so critical, andthe type II hybrid ARQ scheme may be utilised. For each type II
scheme, the minimum required Eb=N0 is attained after all the parity bits
are transmitted. Hence, the optimum puncture period P that minimises
Eb=N0 depends on Imax. When Imax ¼ 4, the minimum Eb=N0 is 4 dB
and is achieved by S-P2. When Imax can be as large as 5 or 6, S-P4 isthe best. However if Imax > 8 is allowed, S-P8 is the most desirable
scheme.

Conclusion: The performance of RCPT coded hybrid ARQ for
DS-CDMA in a frequency selective Rayleigh fading channel wasevaluated when the number of allowable retransmissions is limited. It
has been found that the type II hybrid ARQ S-P8 is the mostfavourable in order to maximise throughput. If signal energy is tobe kept low, the best scheme depends on the maximum number Imax oftransmissions allowed: the type I scheme is the best for delay sensitive
real-time application and type II is suitable for delay tolerant applications such as packet data communications. In type II ARQ schemes,
the minimum required Eb=N0 is attained after all the parity bits aretransmitted and depends on P. Therefore the optimum P depends onImax.
# IEE 2003
Electronics Letters Online No: 20030177
DOI: 10.1049/el:20030177

13 November 2002

D. Garg, R. Kimura and F. Adachi (Department of Electrical andCommunication Engineering, Graduate School of Engineering,Tohoku University, 05 Aza-Aoba, Aramaki, Aoba-ku, Sendai
980-8579, Japan)
E-mail: deep@mobile.ecei.tohoku.ac.jp
References
1

2

3

ROWITCH, D.N., and MILSTEIN, L.B.: ‘Rate compatible punctured turbo(RCPT) codes in hybrid FEC=ARQ system’. Proc. Communication
Theory, Mini-conference of GLOBECOM’97, November 1997,
pp. 55–59
JI, T., and STARK, W.E.: ‘Turbo-coded ARQ schemes for DS-CDMA datanetworks over fading and shadowing channels: throughput, delay
and energy efficiency’, IEEE J. Sel. Areas Commun., 2000, 18,
pp. 1355–1364
ANDOH, H., SAWAHASHI, M., and ADACHI, F.: ‘Channel estimation
filter using time-multiplexed pilot channel for coherent RAKE
combining in DS-CDMA mobile radio’, IEICE Trans. Commun., 1998,
E81-B, pp. 1517–1526

ELECTRONICS LETTERS

23rd January 2003

Vol. 39 No. 2