Quantization. Absorbing Regions and Practical Message Passing Decoders

Low-density parity-check (LDPC) codes and accompanying message passing decoding algorithms are a popular choice for data encoding and decoding in modem communications and storage systems. To reduce implementation complexity, the messages in a practical message passing decoder are necessarily quantized. It is well known that the performance of practical, quantized message passing decoders in the high-reliability regime is governed by non-codeword decoding errors, typically described via trapping/absorbing sets. Absorbing regions act as "decoding regions" around absorbing sets. In this work, we take a closer look at the interplay between quantization and absorbing regions. We provide a study of a range of quantization choices, describe the impact of quantization on the candidate absorbing regions, and derive guidelines for practical finite-precision decoders. In particular, we show that, depending on the choice of the quantization allocation, different absorbing sets emerge as dominant: even though the overall performance of two quantization schemes can be similar, the distribution of decoding errors across possible absorbing sets can be substantially different. We take the advantage of disjointness of error profiles of two carefully chosen quantized decoders to design a decoder that is a series of these two decoders. T he result is a performance improvement of at least an order magnitude relative to constituent decoders without increase in complexity.