Approaching Shannon's capacity limit by 0.27 dB using Hamming codes in a `turbo'-decoding scheme

The Shannon capacity limit can be reached by less than 0.27 dB at a BER of 10 \Gamma5 by applying long but simple Hamming codes as component codes to an iterative `turbo'--decoding scheme. In general, the complexity of soft--in/soft--out decoding of binary block codes is rather high. However, the application of a neurocomputer in combination with a parallelization of the decoding rule facilitates an implementation of the decoding algorithm in the logarithmic domain which requires only matrix additions and multiplications. I. introduction Recently, interest has focused on iterative decoding of two and more dimensional product-like codes, which has been termed `turbo'- codes [1]. The basic concept of this new (de)coding scheme is to use a parallel concatenation of at least two binary codes in an interleaved scheme. Decoding is based on alternately decoding the component codes and passing the so--called extrinsic information being part of the soft output of the soft in/soft out decod..