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An MCMC Approach to Universal Lossy Compression of Analog Sources
Motivated by the Markov chain Monte Carlo (MCMC) approach to the compression
of discrete sources developed by Jalali and Weissman, we propose a lossy
compression algorithm for analog sources that relies on a finite reproduction
alphabet, which grows with the input length. The algorithm achieves, in an
appropriate asymptotic sense, the optimum Shannon theoretic tradeoff between
rate and distortion, universally for stationary ergodic continuous amplitude
sources. We further propose an MCMC-based algorithm that resorts to a reduced
reproduction alphabet when such reduction does not prevent achieving the
Shannon limit. The latter algorithm is advantageous due to its reduced
complexity and improved rates of convergence when employed on sources with a
finite and small optimum reproduction alphabet.Comment: 21 pages, submitted for publicatio