HagenauerIterativeDecoding - IEEE TRANSACTIONS ON...

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IEEE TRANSACTIONS ON INFORMATION THEORY, VOL. 42, NO. 2, MARCH 1996 429 Iterative Decoding of Binary Block and Convolutional Codes Joachim Hagenauer, Fellow, ZEEE, Elke Offer, and Lutz Papke Abstract- Iterative decoding of two-dimensional systematic convolutional codes has been termed “turbo ” (de)coding. Using log-likelihood algebra, we show that any decoder can he used which accepts soft inputs-including a priori values-and delivers soft outputs that can he split into three terms: the soft channel and a priori inputs, and the extrinsic value. The extrinsic value is used as an a priori value for the next iteration. Decoding algorithms in the log-likelihood domain are given not only for convolutional codes hut also for any linear binary block code. The iteration is controlled by a stop criterion derived from cross entropy, which results in a minimal number of iterations. Optimal and suboptimal decoders with reduced complexity are presented. Simulation results show that very simple component codes are sufficient, block codes are appropriate for high rates and convolutional codes for lower rates less than 213 . Any combination of block component codes is possible. Several interleaving techniques are described. At a bit error rate (BER) of lo-* the performance is slightly above or around the bounds given by the cutoff rate for reasonably simple block/convolutional codes, interleaver sizes less than 1000 and for three to six iterations. Index Terms- Concatenated codes, product codes, iterative decoding, “soft-inlsoft-out ” decoder, “turbo ” (de)coding. I. INTRODUCTION S INCE the early days of information and coding theory the goal has always been to come close to the Shannon limit performance with a tolerable complexity. The results achieved so far show that it is relatively easy to operate at signal- to-noise ratios of &/No above the value determined by the channel cutoff rate. For a rate l/2 code and soft decisions on a binary input additive white Gaussian noise (AWGN) channel the cutoff rate bound is at 2.5 dB, as opposed to the capacity limit which for rate l/2 is at 0.2 dB. It is generally held that between those two values of &/No the task becomes very complex. Previously known methods of breaking this barrier were a) sequential decoding with the drawback of time and/or storage overflow and b) concatenated coding using Viterbi and ReedSolomon decoders which achieve 1.6 dB at the cost of a large interleaver and feedback between two decoders [ 11. Recently, interest has focused on iterative decoding of prod- uct or concatenated codes using “soft-in/soft-out ” decoders Manuscript received September 7, 1994; revised August 20, 1995. J. Hagenauer is with the Technical University of Munich, D-80290 Munich, Germany. E. Offer and L. Papke are with the Institute for Communications Technol- ogy, German Aerospace Research Establishment (DLR), Oberpfaffenhofen, D-82230 Wessling, P.O. Box 1116, Germany. Publisher Item Identifier S 0018-9448(96)01474-5. with fairly simple component codes in an interleaved scheme.
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HagenauerIterativeDecoding - IEEE TRANSACTIONS ON...

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