Tree-structure Expectation Propagation for Decoding LDPC codes over Binary Erasure Channels

TL;DR

This paper introduces a novel decoding algorithm for LDPC codes over binary erasure channels that enhances decoding capability by imposing pair-wise marginal constraints, outperforming traditional belief propagation especially at finite block sizes.

Contribution

It proposes a tree-structure expectation propagation algorithm that improves LDPC decoding by adding pair-wise constraints, matching BP complexity and surpassing it in erasure correction.

Findings

Decoding ability increases with larger block sizes.

Algorithm outperforms BP decoder at finite block sizes.

Complexity remains identical to BP decoding.

Abstract

Expectation Propagation is a generalization to Belief Propagation (BP) in two ways. First, it can be used with any exponential family distribution over the cliques in the graph. Second, it can impose additional constraints on the marginal distributions. We use this second property to impose pair-wise marginal distribution constraints in some check nodes of the LDPC Tanner graph. These additional constraints allow decoding the received codeword when the BP decoder gets stuck. In this paper, we first present the new decoding algorithm, whose complexity is identical to the BP decoder, and we then prove that it is able to decode codewords with a larger fraction of erasures, as the block size tends to infinity. The proposed algorithm can be also understood as a simplification of the Maxwell decoder, but without its computational complexity. We also illustrate that the new algorithm outperforms the BP decoder for finite block-size