Decoding LDPC codes with mutual information-maximizing lookup tables

A recent result has shown connections between statistical learning theory and channel quantization. In this paper, we present a practical application of this result to the implementation of LDPC decoders. In particular, we describe a technique for designing the message-passing decoder mappings (or lookup tables) based on the ideas of channel quantization. This technique is not derived from sum-product algorithm or any other LDPC decoding algorithm. Instead, the proposed algorithm is based on an optimal quantizer in the sense of maximization of mutual information, which is inserted in the density evolution algorithm to generate the lookup tables. This algorithm has low complexity since it only employs 3-bit messages and lookup tables, which can be easily implemented in hardware. Two quantized versions of the min-sum decoding algorithm are used for comparison. Simulation results for a binary-input AWGN channel show 0.3 dB and 1.2 dB gains versus the two quantized min-sum algorithms. On the binary symmetric channel also a gain is seen.