ABSTRACT
This chapter reviews nonbinary low–density parity–check (NB–LDPC) decoder architectures, with emphasis given to algorithmic and architectural modification techniques for the check node units. The belief propagation (BP) for binary low-density parity-check decoding can be extended to decode NB–LDPC codes. In non–binary BP, the check node processing also computes sums of products of probabilities. The computations in non–binary check node processing can be considered as convolutions of the incoming messages. Multiplications in probability domain are implemented as additions in log domain. The most prominent ones are the extended Minsum algorithm and the Min–max algorithm. Both of them are log-domain algorithms. The approximations lead to slight performance loss compared to the BP, the hardware complexity has been greatly reduced in these algorithms, and only additions on the reliability messages are involved in their check node processing. The number of multiplications in the check node processing is reduced in the frequency–domain approach.
