ITERATIVE DECODING OF BINARY BLOCK AND CONVOLUTIONAL-CODES

Iterative decoding of two-dimensional systematic convolutional codes h as been termed ''turbo'' (de)coding, Using log-likelihood algebra, we show that any decoder can be used which accepts soft inputs-including a priori values-and delivers soft outputs that can be 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 iterati on, Decoding algorithms in the log-likelihood domain are given not onl y for convolutional codes but also for any linear binary systematic bl ock code, The iteration is controlled by a stop criterion derived from cross entropy, which results in a minimal number of iterations, Optim al and suboptimal decoders with reduced complexity are presented, Simu lation results show that very simple component codes are sufficient, b lock codes are appropriate for high rates and convolutional codes for lower rates less than 2/3. Any combination of block and convolutional component codes is possible, Several interleaving techniques are descr ibed, At a bit error rate (BER) of 10(-4) the performance is slightly above or around the bounds given by the cutoff rate for reasonably sim ple block/convolutional component codes, interleaver sizes less than 1 000 and for three to six iterations.