Abstract

n Figure 1. Communication system. Encoder Channel u 1 ,...,u k x 1 ,...,x n Decoder ^ u 1 ,..., ^ u k y 1 ,...,y n n Figure 2. Simple encoder. "Addition" is modulo 2 (exclusive OR). u 1 x 1 u 2 x 2 x 3 IEEE Communications Magazine . April 1999 100 mostly exclusive-OR operations, which are perfectly suited for digital implementation. Probabilistic decoding, on the other hand, uses computations with real numbers, which makes digital implementations of such decoders much more complex than those of algebraic decoders. Moreover, the computation networks of decoders for high-performance codes such as turbo codes and low-density parity check codes contain loops. In digital implementations, these loops lead to iterative computations where the whole network is recomputed several times until a steady state is reached (or until the available time is over). Such iterations are also required if the soft output of the decoder is fed back to other parts of the receiver, as indicated in...

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