Efficient data compression from statistical physics of codes over finite fields

A. Braunstein, F. Kayhan, R. Zecchina
2011 Physical Review E  
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
more » ... words 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.
doi:10.1103/physreve.84.051111 pmid:22181373 fatcat:2pheajtygvfpvp5a7v6h7kczvq