Efficient data compression from statistical physics of codes over finite fields

Abstract

In this paper we discuss a novel data compression technique for binary symmetric sources based on the cavity method over a Galois Field of order q (GF(q)). We present a scheme of low complexity and near optimal empirical performance. The compression step is based on a reduction of sparse low density parity check codes over GF(q) and is done through the so called reinforced belief-propagation equations. These reduced codes appear to have a non-trivial geometrical modification of the space of codewords which makes such compression computationally feasible. The computational complexity is O(d.n.q.log(q)) per iteration, where d is the average degree of the check nodes and n is the number of bits. For our code ensemble, decompression can be done in a time linear in the code's length by a simple leaf-removal algorithm.

10 pages, 4 figures

References in corpus (5)

• Phase Transitions in the Coloring of Random Graphs
• Learning by message-passing in networks of discrete synapses
• Entropy landscape and non-Gibbs solutions in constraint satisfaction problems
• Encoding for the Blackwell Channel with Reinforced Belief Propagation
• Typical Performance of Irregular Low-Density Generator-Matrix Codes for Lossy Compression

Cited by in corpus (4)

• The large deviations of the whitening process in random constraint satisfaction problems
• A Max-Sum algorithm for training discrete neural networks
• Code optimization, frozen glassy phase and improved decoding algorithms for low-density parity-check codes
• The closest vector problem and the zero-temperature p-spin landscape for lossy compression