Random codes: Minimum distances and error exponents

被引：153

作者：

Barg, A ^{[1
]}

Forney, GD

机构：

[1] Bell Labs, Lucent Technol, Murray Hill, NJ 07974 USA

[2] Inst Informat Transmiss Problems, Moscow, Russia

[3] MIT, Cambridge, MA 02139 USA

来源：

IEEE TRANSACTIONS ON INFORMATION THEORY | 2002年 / 48卷 / 09期

关键词：

distance distributions; exponential error bounds; minimum distance; random codes; random linear codes; typical linear codes; typical random codes;

D O I：

10.1109/TIT.2002.800480

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

Minimum distances, distance distributions, and error exponents on a binary-symmetric channel (BSC) are given for typical codes from Shannon's random code ensemble and for typical codes from a random linear code ensemble. A typical random code of length N and rate R is shown to have minimum distance Ndelta(GV) (2R), where delta(GV) (R) is the Gilbert-Varshamov (GV) relative distance at rate R, whereas a typical linear code (TLC) has minimum distance Ndelta(GV) (R). Consequently, a TLC has a better error exponent on a BSC at low rates, namely, the expurgated error exponent.

引用

页码：2568 / 2573

页数：6

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