2006•Unpublished venueRequires access

Toward a Source Coding Theory for Sets

Lav R. Varshney, Vivek K Goyal

Abstract

The problem of communicating (unordered) sets, rather than (ordered) sequences is formulated. Elementary results in all major branches of source coding theory, including lossless coding, high-rate and low-rate quantization, and rate distortion theory are presented. In certain scenarios, rate savings of log n! bits for sets of size n are obtained. Asymptotically in the set size, the entropy rate is zero and for sources with an ordered parent alphabet, the (0,0) point is the rate distortion function.

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Key concepts: Rate distortion, Rate–distortion theory, Entropy encoding, Alphabet, Entropy (arrow of time), Coding (social sciences), Mathematics, Source code