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• W2079778722 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 $O(dnq{mathrm{log}}_{2}q)$ 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." @default.
• W2079778722 created "2016-06-24" @default.
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• W2079778722 date "2011-11-14" @default.
• W2079778722 modified "2023-10-16" @default.
• W2079778722 title "Efficient data compression from statistical physics of codes over finite fields" @default.
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• W2079778722 doi "https://doi.org/10.1103/physreve.84.051111" @default.
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