This article is cited in 14 papers

Information Theory

The sphere packing bound for memoryless channels

B. Nakiboğlu

Middle East Technical University, Ankara, Turkey

Abstract: Sphere packing bounds (SPBs)—with prefactors that are polynomial in the block length—are derived for codes on two families of memoryless channels using Augustin’s method: (possibly nonstationary) memoryless channels with (possibly multiple) additive cost constraints and stationary memoryless channels with convex constraints on the composition (i.e., empirical distribution, type) of the input codewords. A variant of Gallager’s bound is derived in order to show that these sphere packing bounds are tight in terms of the exponential decay rate of the error probability with the block length under mild hypotheses.

Keywords: Augustin’s method, sphere packing exponent, error exponent, reliability function, memoryless channels, Gaussian channels, Poisson channels.

UDC: 621.391.1 : 519.72

Received: 18.04.2018
Revised: 06.03.2020
Accepted: 29.04.2020

DOI: 10.31857/S0555292320030018

 English version: Problems of Information Transmission, 2020, 56:3, 201–244

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