Bounds on the Reliability of a Typewriter Channel

Marco Dalai; Yury Polyanskiy

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arXiv · 1607.05064

Bounds on the Reliability of a Typewriter Channel

Marco Dalai·Yury Polyanskiy

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Abstract

We give new bounds on the reliability function of a typewriter channel with 5 inputs and crossover probability $1/2$. The lower bound is more of theoretical than practical importance; it improves very marginally the expurgated bound, providing a counterexample to a conjecture on its tightness by Shannon, Gallager and Berlekamp which does not need the construction of algebraic-geometric codes previously used by Katsman, Tsfasman and Vl\u{a}du\c{t}. The upper bound is derived by using an adaptation of the linear programming bound and it is essentially useful as a low-rate anchor for the straight line bound.

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Marco Dalai, Yury Polyanskiy. 2016-07-18. Bounds on the Reliability of a Typewriter Channel. https://arxiv.org/abs/1607.05064

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