Channel coding rate in the finite blocklength regime

Yury Polyanskiy; H. Vincent Poor; Sergio Verdu

doi:10.1109/TIT.2010.2043769

Channel coding rate in the finite blocklength regime

Yury Polyanskiy, H. Vincent Poor, Sergio Verdu

Research output: Contribution to journal › Article › peer-review

2191 Scopus citations

Abstract

This paper investigates the maximal channel coding rate achievable at a given blocklength and error probability. For general classes of channels new achievability and converse bounds are given, which are tighter than existing bounds for wide ranges of parameters of interest, and lead to tight approximations of the maximal achievable rate for blocklengths n as short as 100. It is also shown analytically that the maximal rate achievable with error probability ε is closely approximated by C - √V/n Q^-1 (ε) where C is the capacity, V is a characteristic of the channel referred to as channel dispersion, and Q is the complementary Gaussian cumulative distribution function.

Original language	English (US)
Article number	21
Pages (from-to)	2307-2359
Number of pages	53
Journal	IEEE Transactions on Information Theory
Volume	56
Issue number	5
DOIs	https://doi.org/10.1109/TIT.2010.2043769
State	Published - May 2010

All Science Journal Classification (ASJC) codes

Information Systems
Computer Science Applications
Library and Information Sciences

Keywords

Achievability
Channel capacity
Coding for noisy channels
Converse
Finite blocklength regime
Shannon theory

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10.1109/TIT.2010.2043769

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abstract = "This paper investigates the maximal channel coding rate achievable at a given blocklength and error probability. For general classes of channels new achievability and converse bounds are given, which are tighter than existing bounds for wide ranges of parameters of interest, and lead to tight approximations of the maximal achievable rate for blocklengths n as short as 100. It is also shown analytically that the maximal rate achievable with error probability ε is closely approximated by C - √V/n Q-1 (ε) where C is the capacity, V is a characteristic of the channel referred to as channel dispersion, and Q is the complementary Gaussian cumulative distribution function.",

keywords = "Achievability, Channel capacity, Coding for noisy channels, Converse, Finite blocklength regime, Shannon theory",

author = "Yury Polyanskiy and Poor, {H. Vincent} and Sergio Verdu",

note = "Funding Information: Manuscript received November 14, 2008; revised October 22, 2009. Current version published April 21, 2010. This work was supported in part by the National Science Foundation by Grants Grants CCF-06-35154, CCF-07-28445, and CNS-09-05398. The authors are with the Department of Electrical Engineering, Princeton University, Princeton, NJ 08544 USA (e-mail: ypolyans@princeton.edu; poor@princeton.edu; verdu@princeton.edu). Communicated by G. Kramer, Associate Editor for Shannon Theory. Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TIT.2010.2043769",

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AU - Poor, H. Vincent

AU - Verdu, Sergio

N1 - Funding Information: Manuscript received November 14, 2008; revised October 22, 2009. Current version published April 21, 2010. This work was supported in part by the National Science Foundation by Grants Grants CCF-06-35154, CCF-07-28445, and CNS-09-05398. The authors are with the Department of Electrical Engineering, Princeton University, Princeton, NJ 08544 USA (e-mail: ypolyans@princeton.edu; poor@princeton.edu; verdu@princeton.edu). Communicated by G. Kramer, Associate Editor for Shannon Theory. Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TIT.2010.2043769

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N2 - This paper investigates the maximal channel coding rate achievable at a given blocklength and error probability. For general classes of channels new achievability and converse bounds are given, which are tighter than existing bounds for wide ranges of parameters of interest, and lead to tight approximations of the maximal achievable rate for blocklengths n as short as 100. It is also shown analytically that the maximal rate achievable with error probability ε is closely approximated by C - √V/n Q-1 (ε) where C is the capacity, V is a characteristic of the channel referred to as channel dispersion, and Q is the complementary Gaussian cumulative distribution function.

AB - This paper investigates the maximal channel coding rate achievable at a given blocklength and error probability. For general classes of channels new achievability and converse bounds are given, which are tighter than existing bounds for wide ranges of parameters of interest, and lead to tight approximations of the maximal achievable rate for blocklengths n as short as 100. It is also shown analytically that the maximal rate achievable with error probability ε is closely approximated by C - √V/n Q-1 (ε) where C is the capacity, V is a characteristic of the channel referred to as channel dispersion, and Q is the complementary Gaussian cumulative distribution function.

KW - Achievability

KW - Channel capacity

KW - Coding for noisy channels

KW - Converse

KW - Finite blocklength regime

KW - Shannon theory

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Channel coding rate in the finite blocklength regime

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