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

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

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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 “non-standard” procedures or computations. Here we follow Blinovsky’s idea of using a Ramsey-theoretic result by Komlós, 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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《IEEE Transactions on Information Theory》 |2022年第5期|2829-2838|共10页
作者
Marco Bondaschi; Marco Dalai;
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作者单位

School of Computer and Communication Sciences, école Polytechnique Fédérale de Lausanne, Lausanne, Switzerland;

University of Brescia, Via Branze, Brescia, Italy;

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正文语种英语
中图分类通信;
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Codes; Maximum likelihood decoding; Upper bound; Memoryless systems; Probability distribution; Limiting; Electronic mail;

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

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