Non-surjective finite alphabet iterative decoders

This paper introduces a new theoretical framework, akin to the use of imprecise message storage in Low Density Parity Check (LDPC) decoders, which is seen as an enabler for cost-effective hardware designs. The proposed framework is the one of Non-Surjective Finite Alphabet Iterative Decoders (NS-FAIDs), and it is shown to provide a unified approach for several designs previously proposed in the literature. NS-FAIDs are optimized by density evolution for WiMAX irregular LDPC codes and we show they provide different trade-offs between hardware complexity and decoding performance. In particular, we derive a set of 27 NS-FAIDs that provide decoding gains up to 0.36 dB, while yielding a memory/interconnect reduction up to 25%/30% compared to the Min-Sum decoder.