Two-Bit Message Passing Decoders for LDPC Codes Over the Binary Symmetric Channel

In this paper, the authors consider quantized decoding of LDPC codes on the binary symmetric channel. The binary message passing algorithms, while allowing extremely fast hardware implementation, are not very attractive from the perspective of performance. More complex decoders such as the ones based on belief propagation exhibit superior performance but lead to slower decoders. The approach in this paper is to consider message passing decoders that have larger message alphabet (thereby providing performance improvement) as well as low complexity (thereby ensuring fast decoding). They propose a class of message-passing decoders whose messages are represented by two bits. The thresholds for various decoders in this class are derived using density evolution.