Multiple turbo codes

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Abstract
In this paper, we introduce multiple turbo codes and a suitable decoder structure derived from an approximation to the maximum a posteriori probability (MAP) decision rule, which is substantially difierent from the decoder for two-code-based en- coders. We developed new rate 1/3 and 2/3 constituent codes to be used in the turbo encoder structure. These codes, for 2 to 32 states, are designed by using primitive polynomials. The resulting turbo codes have rates b=n , b =1 ; 2 and n =3 ; 4, and include random interleavers for better asymptotic performance. A rate 2/4 code with 16QAM modulation was used to realize a turbo trellis coded modulation (TTCM) scheme at 2 bit/sec/Hz throughput, whose performance is within 1 dB from the Shannon limit at BER=10 ¡ 5 . I. Introduction Coding theorists have traditionally attacked the problem of de- signing good codes by developing codes with a lot of structure, which lends itself to feasible decoders, although coding theory suggests that codes chosen \at random" should perform well if their block size is large enough. The challenge to flnd practical decoders for \almost" random, large codes has not been seriously considered until recently. Perhaps the most exciting and poten- tially important development in coding theory in recent years has been the dramatic announcement of \turbo codes" by Berrou et al. in 1993 (7). The announced performance of these codes was so good that the initial reaction of the coding establishment was deep skepticism, but recently researchers around the world have been able to reproduce those results (15, 18, 9). The introduc- tion of turbo codes has opened a whole new way of looking at the problem of constructing good codes (5) and decoding them with low complexity (7, 2). These codes achieve near-Shannon-limit error correction per- formance with relatively simple component codes and large inter- leavers. A required E b =N o of 0.7 dB was reported for a bit error rate (BER) of 10 ¡ 5 for a rate 1/2 turbo code (7).

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