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arXiv · 1912.04411

A Revisitation of Low-Rate Bounds on the Reliability Function of Discrete Memoryless Channels for List Decoding

Marco Bondaschi·Marco Dalai
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Abstract

We revise the proof of low-rate upper bounds on the reliability function of discrete memoryless channels for ordinary and list-decoding schemes, in particular Berlekamp and Blinovsky's zero-rate bound, as well as Blahut's bound for low rates. The available proofs of the zero-rate bound devised by Berlekamp and Blinovsky are somehow complicated in that they contain in one form or another some cumbersome "non-standard" procedures or computations. Here we follow Blinovsky's idea of using a Ramsey-theoretic result by Komlos, and we complement it with some missing steps to present a proof which is rigorous and easier to inspect. Furthermore, we show how these techniques can be used to fix an error that invalidated the proof of Blahut's low-rate bound, which is here presented in an extended form for list decoding and for general channels.

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Marco Bondaschi, Marco Dalai. 2019-12-09. A Revisitation of Low-Rate Bounds on the Reliability Function of Discrete Memoryless Channels for List Decoding. https://arxiv.org/abs/1912.04411

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