Near Sufficiency of Random Coding for Two Descriptions

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We give a single letter outer bound for the two descriptions problem for iid sources that is universally close to the El Gamal and Cover (EGC) inner bound. The constants characterizing the gaps in the quadratic distortion case for the sum and individual rates are upper bounded by 1.5 and 0.5 bits/sample respectively, and are universal with respect to the source being encoded and the
desired distortion levels, with the assumption that, after normalizing the source to have unit variance, and additionally, Variants of our basic ideas are presented, including upper and lower bounds on the second channel’s rate when the first channel’s rate is arbitrarily close to ; said bounds differ, in the limit as the code block length goes to infinity, by not more than 2 bits/sample. An interesting aspect of our methodology is the manner in which the matching single letter outer bound is obtained, as we eschew common techniques for constructing single-letter bounds in favor of new ideas in the field of rate loss bounds. We expect these techniques to be generally applicable to other settings of interest.

By: Luis Alfonso Lastras-Montaño, Vittorio Castelli

Published in: IEEE Transactions on Information Theory, volume 52, (no 2), pages 681-95 in 2006


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