ISIT2000, Sorrento, Italy, June 25–30, 2000
Bandwidth Efficient Hybrid ARQ Schemes Using Turbo Codes Adrish Banerjee1
Daniel J. Costello Jr.
Thomas E. Fuja
Department of EE, University of Notre Dame, Notre Dame, IN, U.S.A. e-mail:
[email protected]
Department of EE, University of Notre Dame, Notre Dame, IN, U.S.A. e-mail:
[email protected]
Department of EE, University of Notre Dame, Notre Dame,IN, U.S.A. e-mail:
[email protected]
I. Introduction When data is transmitted in the form of packets, it is common to use Automatic Repeat reQuest (ARQ) or retransmission techniques in addition to Forward Error Correction (FEC) to improve the performance of a communication system. Several schemes have been suggested in which code combining retransmission schemes using low rate turbo codes have been shown to yield good performance [1]. Separately, sequence combining TCM schemes have been proposed for systems requiring higher throughputs [2]. In this paper, we present several TTCM schemes for use in ARQ systems, thereby combining the advantages of TCM with those of Turbo codes in a retransmission environment.
II. System Description We assume a selective repeat ARQ scheme with suitably large buffers at the transmitter and receiver. Furthermore, we assume an error free feedback channel over which positive (ACK) or negative (NACK) acknowledgements can be sent. The underlying TTCM scheme used here is the one proposed by Berrou et. al [3]. A coherent receiver model is assumed. The data sequence consists of information bits and a 16-bit CRC sequence. The sequence is fed into the Turbo encoder whose output is punctured to the desired rate and formatted into P-symbol data packets, U = (u1 , · · · uP ), where each symbol ui consists of m bits (i.e., a signal constellation size of 2m ). The following HARQ schemes using TTCM are considered. In Scheme 1, the same packet is retransmitted until the receiver accepts it as error free or until a preset maximum allowed number of retransmission attempts is reached. The error prone packets in the previous transmissions are discarded. In Scheme 2, also known as an average diversity combining scheme, copies of a retransmitted packet are combined into a single packet of the same blocksize by averaging the soft demodulated values of each packet and then decoding. Scheme 3 is an incremental redundancy scheme where received packets are concatenated to form noise-corrupted codewords from increasingly longer and lower rate codes. During the first transmission only the information bits are sent. Subsequently, the check digits are incrementally transmitted to adaptively meet the error performance requirements of the system. Finally, we 1 This work was supported by Motorola Inc., NASA grant NAG 5-8355, NSF grant NCR95-22939, and NSF grant CCR-9996222.
assume the blocksize is the same for all transmissions in order to keep network overhead to a minimum.
III. Numerical Results
Scheme 1 and Scheme 2 employing TTCM use a rate 2/3 Turbo code obtained by puncturing parity bits from a 4-state (7, 5)octal constituent recursive convolutional encoder along with Gray mapping to a 8PSK signal constellation. The turbo decoder uses the APP algorithm. After every iteration, the CRC is checked. Scheme 3 employing TTCM uses a mother turbo code of rate 1/3 mapped to an 8PSK constellation and higher rates are achieved by puncturing. Scheme 1 employing TCM uses a rate 2/3 convolutional encoder obtained by puncturing a rate 1/2 16-state (23, 35)octal convolutional encoder. The throughputs are plotted in Fig.1 for an information blocksize of 512 on an AWGN channel. 3 Scheme 3−TTCM Scheme 1−TTCM Scheme 2−TTCM Scheme 1 TCM
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Abstract — New bandwidth efficient Type-I and Type-II hybrid-ARQ (HARQ) schemes using Turbo Trellis Coded Modulation (TTCM) are proposed. These schemes combine the power-efficiency of turbo codes with the bandwidth efficiency of Trellis Coded Modulation (TCM) to give efficient FEC/ARQ system designs.
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Fig. 1: Throughput comparison of various schemes
IV. Conclusions In this paper, a new application of turbo codes to bandwidth efficient ARQ schemes is introduced. Since the combining schemes described here use a single decoder to decode any received packet or any combination of received packets, the implementation of these protocols requires only minor modifications to the transmitting and receiving systems of a standard turbo code.
References [1] K. Narayanan and G. Stuber, “Turbo decoding for packet data systems,” Communication Theory Mini-Conference, GLOBECOMM 97, pp 44-48, 1997. [2] R. H. Deng, “Hybrid ARQ schemes employing coded modulation and sequence combining,” IEEE Transactions on Communications , vol. 42, pp. 2239-2245, 1994. [3] S.L. Goff, A. Glavieux, and C. Berrou, “Turbo-codes and high spectral efficiency modulation,” ICC 94 , pp. 645-649, 1994.
