Rate-Distortion via Markov Chain Monte Carlo

We propose an approach to lossy source coding, utilizing ideas from Gibbs sampling, simulated annealing, and Markov Chain Monte Carlo (MCMC). The idea is to sample a reconstruction sequence from a Boltzmann distribution associated with an energy function that incorporates the distortion between the source and reconstruction, the compressibility of the reconstruction, and the point sought on the rate-distortion curve. To sample from this distribution, we use a 'heat bath algorithm': Starting from an initial candidate reconstruction (say the original source sequence), at every iteration, an index i is chosen and the i-th sequence component is replaced by drawing from the conditional probability distribution for that component given all the rest. At the end of this process, the encoder conveys the reconstruction to the decoder using universal lossless compression. The complexity of each iteration is independent of the sequence length and only linearly dependent on a certain con...

• Type: Journal
• Year: 2008
• Where: CORR
• Authors: Shirin Jalali, Tsachy Weissman
• Keywords: CORR 2008, Education, Markov Chain Monte Carlo, Reconstruction Sequence, Sequence Length