Exponential Error Bounds on Codes for Noisy Channels with Inaccurately Known Statistics and for Generalized Decision Rules
Abstract
Generalized decoding decision rules provide added flexibility in a decoding scheme and some advantages. In a generalized decoding decision rule, the following possibilities are considered: (1) The decoder has the option of not deciding at all, or rejecting all estimates. This is termed an erasure; (2) The decoder has the option of putting out more than one estimate. The resulting output is called a list. Only if the correct code word is not on the list do we have a list error. Foreney developed error bounds in his seminal paper of 1968 in which he used Gallager's ingenious 1965 method of bounding error probabilities. In this paper, we consider another realistic factor, the lack of exact knowledge of the channel statistics. We assume a mismatch between the true channel transition probabilities and the nominal probabilities used in the decoding metric. We then develop error bounds under mismatch for generalized decision rules. We also establish conditions under which the error probabilities converge to zero exponentially with the block length, in spite of the presence of mismatch.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 01, 1992
- Accession Number
- ADA246064
Entities
People
- A. B. Cooper Iii
- D. Kazakos
Organizations
- Ballistic Research Laboratory