title: 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 GF(q), the Galois Field of order q. We present a scheme of low complexity and near-optimal empirical performance. The compression step is based on a reduction of a sparse low-density parity-check code over GF(q) and is done through the so-called reinforced belief-propagation equations. These reduced codes appear to have a nontrivial geometrical modification of the space of codewords, which makes such compression computationally feasible. The computational complexity is O(dnqlog(2)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.
authors.affiliation: Dipartimento di Fisica and Center for Computational Sciences, Politecnico di Torino, Torino, Italy.
authors.forename: A
authors.initials: A
authors.lastname: Braunstein
authors.forename: F
authors.initials: F
authors.lastname: Kayhan
authors.forename: R
authors.initials: R
authors.lastname: Zecchina