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(dnqlog2q) 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.
Efficient data compression from statistical physics of codes over finite fields / Braunstein, Alfredo; Kayhan, Farbod; Zecchina, Riccardo. - In: PHYSICAL REVIEW E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS. - ISSN 1539-3755. - STAMPA. - 84:(2011), p. 051111. [10.1103/PhysRevE.84.051111]
Efficient data compression from statistical physics of codes over finite fields
BRAUNSTEIN, ALFREDO;KAYHAN, FARBOD;ZECCHINA, RICCARDO
2011
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(dnqlog2q) 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.Pubblicazioni consigliate
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https://hdl.handle.net/11583/2460654
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