Analysis of Quasi-Cyclic LDPC codes under ML decoding over the erasure channel

TL;DR

This paper demonstrates that Quasi-Cyclic LDPC codes can be efficiently decoded over the erasure channel using a hybrid iterative/ML approach, leveraging their structure to reduce decoding complexity while maintaining near-optimal error correction.

Contribution

The paper introduces a method to transform QC-LDPC parity-check matrices into a pseudo-band form, enabling efficient ML decoding with reduced complexity.

Findings

Significant reduction in ML decoding complexity for QC-LDPC codes.

Near-ideal error correction performance achieved under ML decoding.

Decoding complexity scales as $k\sqrt{k}$, where $k$ is the number of source symbols.

Abstract

In this paper, we show that Quasi-Cyclic LDPC codes can efficiently accommodate the hybrid iterative/ML decoding over the binary erasure channel. We demonstrate that the quasi-cyclic structure of the parity-check matrix can be advantageously used in order to significantly reduce the complexity of the ML decoding. This is achieved by a simple row/column permutation that transforms a QC matrix into a pseudo-band form. Based on this approach, we propose a class of QC-LDPC codes with almost ideal error correction performance under the ML decoding, while the required number of row/symbol operations scales as $k\sqrt{k}$, where $k$ is the number of source symbols.