Random codes: minimum distances and error exponents

Abstract

We consider the average and typical performance of random binary codes of length N and size M=e/sup NR/ from Shannon's random code ensemble (RCE) and from a random linear code ensemble (LCE), on a binary symmetric channel (BSC) with error probability p. These are among the oldest topics in information theory, and most of our results are "known," although not "well known" in the sense of being readily accessible in textbooks, or even in the research literature.