Low complexity Soft-Input Soft-Output Hamming Decoder

We investigate a low complexity Soft-Input Soft-Output (SISO) Hamming Decoder. The Decoding is based on error patterns which belong to the same syndrome. It is shown that it is sufficient to investigate error patterns with one and two errors to gain up to 1:35 dB compared to hard decision decoding. The proposed decoding algorithm has a linearly rising complexity, O(N_c), with the code word length N_c. The further consideration of error patterns with three errors which belong to the determined syndrome gain further 0.2 dB and improves the quality of the soft-output due to the increased number of comparisons with valid code words. However, this also increases the complexity of the decoding process to O(N_c²). We present simulation results for soft decoding of Hamming codes up to a code word length of 63 bit. Furthermore, we present results for turbo decoding with the 63, 57-Hamming code as a component code.