On the asymptotic accuracy of the union bound
Abstract
Description
A new lower bound on the error probability of maximum likelihood decoding of a binary code on a binary symmetric channel was proved in Barg and McGregor (2004, cs.IT/0407011). It was observed in that paper that this bound leads to a new region of code rates in which the random coding exponent is asymptotically tight, giving a new region in which the reliability of the BSC is known exactly. The present paper explains the relation of these results to the union bound on the error probability.
10 pages, 3 figures. Presented at the 42nd Annual Allerton Conference on Communication, Control and Computing (Sept. 29 - Oct. 1, 2004). The paper will appear in the conference proceedings. Version 2 differs slightly from the published version and is the latest version of this paper
10 pages, 3 figures. Presented at the 42nd Annual Allerton Conference on Communication, Control and Computing (Sept. 29 - Oct. 1, 2004). The paper will appear in the conference proceedings. Version 2 differs slightly from the published version and is the latest version of this paper