Alphabet Sizes of Auxiliary Variables in Canonical Inner Bounds

Details Alphabet Sizes of Auxiliary Variables in Canonical Inner Bounds Alphabet Sizes of Auxiliary Variables in Canonical Inner Bounds

2008-10-10

arxiv.org/abs/0810.1973v1

Computer Science

Information Theory

20 pages, no figures, explanation of a part of impending IEEE IT submission

Scientific paper

Alphabet size of auxiliary random variables in our canonical description is derived. Our analysis improves upon estimates known in special cases, and generalizes to an arbitrary multiterminal setup. The salient steps include decomposition of constituent rate polytopes into orthants, translation of a hyperplane till it becomes tangent to the achievable region at an extreme point, and derivation of minimum auxiliary alphabet sizes based on Caratheodory's theorem.

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