Block and Sliding-Block Lossy Compression via MCMC

We propose an approach to lossy compression of finite-alphabet sources that utilizes Markov chain Monte Carlo (MCMC) and simulated annealing methods. The idea is to define an energy function over the space of reconstruction sequences. The energy of a candidate reconstruction sequence is defined such...

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Bibliographic Details
Published inIEEE transactions on communications Vol. 60; no. 8; pp. 2187 - 2198
Main Authors Jalali, Shirin, Weissman, Tsachy
Format Journal Article
LanguageEnglish
Published New York, NY IEEE 01.08.2012
Institute of Electrical and Electronics Engineers
Subjects
Applied sciences
Coding, codes
Compression algorithms
Encoding
Entropy
Exact sciences and technology
Gibbs sampler
Information, signal and communications theory
Markov chain Monte Carlo
Markov processes
Rate-distortion
Rate-distortion coding
Signal and communications theory
Simulated annealing
Telecommunications and information theory
universal lossy compression
Vectors
Alphabet
Lossy compression
Performance evaluation
Block code
Energy function
Rate distortion theory
Ergodicity
Iterative method
Gibbs sampling
Gibbs sampler
MCMC algorithm
Coding
universal lossy compression
Markov chain Monte Carlo
Simulated annealing
Rate-distortion coding
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Summary:We propose an approach to lossy compression of finite-alphabet sources that utilizes Markov chain Monte Carlo (MCMC) and simulated annealing methods. The idea is to define an energy function over the space of reconstruction sequences. The energy of a candidate reconstruction sequence is defined such that it incorporates its distortion relative to the source sequence, its compressibility, and the point sought on the rate-distortion curve. The proposed algorithm samples from the Boltzmann distribution associated with this energy function using the "heat-bath" algorithm. The complexity of each iteration is independent of the sequence length and is only linearly dependent on a certain context parameter, which grows sub-logarithmically with the sequence length. We show that the proposed algorithm achieves optimum rate-distortion performance in the limits of large number of iterations, and sequence length, when employed on any stationary ergodic source. Inspired by the proposed block-coding algorithm, we also propose an algorithm for constructing sliding-block (SB) codes using similar ideas.
ISSN:0090-6778
DOI:10.1109/TCOMM.2012.061412.110194