Ternary Message Passing Decoding of High-Rate Regular LDPC Codes

In this letter, we present an improved ternary message passing (TMP) decoding scheme designed for the high-rate regular low-density parity-check (LDPC) codes, which are widely used in storage systems. The decoders in this approach transmit information internally by only three states, and compared to traditional normalized min-sum decoding, it retains only sign multiplication operations, resulting in lower complexity. Meanwhile, we propose a method for optimizing decoder parameters using the density evolution (DE) analysis, which allows the TMP decoders to achieve performance close to that of the belief propagation decoders. Furthermore, in the case of hard decision inputs, we introduce a quantized DE analysis to optimize and compute decoder parameters, enabling the TMP decoders to even outperform the normalized min-sum decoders.