An Implementable Scheme for Universal Lossy Compression of Discrete Markov Sources

We present a new lossy compressor for discrete sources. For coding a source sequence xn , the encoder starts by assigning a certain cost to each reconstruction sequence. It then finds the reconstruction that minimizes this cost and describes it losslessly to the decoder via a universal lossless compressor. The cost of a sequence is given by a linear combination of its empirical probabilities of some order k + 1 and its distortion relative to the source sequence. The linear structure of the cost in the empirical count matrix allows the encoder to employ a Viterbi-like algorithm for obtaining the minimizing reconstruction sequence simply. We identify a choice of coefficients for the linear combination in the cost function which ensures that the algorithm universally achieves the optimum rate-distortion performance of any Markov source in the limit of large n, provided k is increased as o(log n).

• Type: Conference
• Year: 2009
• Where: DCC
• Authors: Shirin Jalali, Andrea Montanari, Tsachy Weissman
• Keywords: Computer Graphics, DCC 2009, Linear Combination, Reconstruction Sequence, Source Sequence Xn