Sparse Decoding of Low Density Parity Check Codes Using Margin Propagation

One of the key factors underlying the popularity of Low-density parity-check (LDPC) code is its iterative decoding algorithm that is amenable to efficient hardware implementation. Even though different variants of LDPC iterative decoding algorithms have been studied for its error-correcting properties, an analytical basis for evaluating energy efficiency of LDPC decoders has not been reported. In this paper, we present a framework of a parameterized LDPC decoding algorithm that can be optimized to produce sparse representation of communication messages used in iterative decoding. The sparsity of messages is determined by its differential entropy and has been used as a theoretical metric for determining the energy efficiency of an iterative LDPC decoder. At the core of the proposed algorithm is margin propagation (MP) which approximates the log-sum-exp function used in conventional sum-product (SP) decoders by a piecewise linear (PWL) function. Using Monte-Carlo simulations, we demonstrate that the MP decoding leads to a significant reduction in message entropy compared to a conventional SP decoder, while incurring a negligible performance penalty (less than 0.03 dB). The proposed work therefore lays the foundation for design of parameterized LDPC decoders whose bit-error-rate performance can be effectively traded-off with respect to different energy efficiency constraints as required by different set of applications.