Decoder diversity architectures for finite alphabet iterative decoders

We present a finite alphabet iterative decoders (FAIDs), a new type of decoders for low-density parity check (LDPC) codes, which outperform much more complex belief-propagation-based counterparts in the error floor region. The FAID variable node update is a simple Boolean map, and we show that by varying this map one can achieve a class of decoders capable of correcting wide range of distinct error patterns uncorrectable by a single FAID. We call this concept decoding diversity, and present a low-complexity architecture and error performance analysis of the FAID diversity decoder for column-weight three LDPC codes on the binary symmetric channel.