Efficient LDPC Codes over GF(q) for Lossy Data Compression

TL;DR

This paper introduces a low-complexity lossy compression scheme for binary sources using ultra-sparse LDPC codes over GF(q), achieving near-optimal performance with efficient encoding and decoding algorithms.

Contribution

It proposes a novel compression scheme based on b-reduced ultra-sparse LDPC codes over GF(q) with a reinforced belief propagation algorithm for encoding.

Findings

Achieves near-optimal empirical performance.

Encoding complexity is O(<d>.n.q.log q).

Decoding complexity is O(n) for sparse matrices.

Abstract

In this paper we consider the lossy compression of a binary symmetric source. We present a scheme that provides a low complexity lossy compressor with near optimal empirical performance. The proposed scheme is based on b-reduced ultra-sparse LDPC codes over GF(q). Encoding is performed by the Reinforced Belief Propagation algorithm, a variant of Belief Propagation. The computational complexity at the encoder is O(<d>.n.q.log q), where <d> is the average degree of the check nodes. For our code ensemble, decoding can be performed iteratively following the inverse steps of the leaf removal algorithm. For a sparse parity-check matrix the number of needed operations is O(n).