# Lossy compression of discrete sources via Viterbi algorithm - Computer Science > Information Theory

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Abstract: We present a new lossy compressor for discrete-valued sources. For coding asequence $x^n$, the encoder starts by assigning a certain cost to each possiblereconstruction sequence. It then finds the one that minimizes this cost anddescribes it losslessly to the decoder via a universal lossless compressor. Thecost of each sequence is a linear combination of its distance from the sequence$x^n$ and a linear function of its $k^{ m th}$ order empirical distribution.The structure of the cost function allows the encoder to employ the Viterbialgorithm to recover the minimizer of the cost. We identify a choice of thecoefficients comprising the linear function of the empirical distribution usedin the cost function which ensures that the algorithm universally achieves theoptimum rate-distortion performance of any stationary ergodic source in thelimit of large $n$, provided that $k$ diverges as $o\log n$. Iterativetechniques for approximating the coefficients, which alleviate thecomputational burden of finding the optimal coefficients, are proposed andstudied.

Author: ** Shirin Jalali, Andrea Montanari, Tsachy Weissman**

Source: https://arxiv.org/