Next Article in Journal
A Bayesian Approach to the Balancing of Statistical Economic Data
Next Article in Special Issue
Localization of Discrete Time Quantum Walks on the Glued Trees
Previous Article in Journal
One Antimatter— Two Possible Thermodynamics
Previous Article in Special Issue
Prediction Method for Image Coding Quality Based on Differential Information Entropy
Article Menu

Export Article

Open AccessArticle
Entropy 2014, 16(3), 1211-1242; doi:10.3390/e16031211

The Maximum Error Probability Criterion, Random Encoder, and Feedback, in Multiple Input Channels

The State Key Lab. of ISN, Xidian University, No. 2 Taibai South Road, Xi'an 710071, China
Received: 30 October 2013 / Revised: 10 December 2013 / Accepted: 24 December 2013 / Published: 25 February 2014
(This article belongs to the Special Issue Advances in Information Theory)

Abstract

For a multiple input channel, one may define different capacity regions, according to the criterions of error, types of codes, and presence of feedback. In this paper, we aim to draw a complete picture of relations among these different capacity regions. To this end, we first prove that the average-error-probability capacity region of a multiple input channel can be achieved by a random code under the criterion of maximum error probability. Moreover, we show that for a non-deterministic multiple input channel with feedback, the capacity regions are the same under two different error criterions. In addition, we discuss two special classes of channels to shed light on the relation of different capacity regions. In particular, to illustrate the roles of feedback, we provide a class of MAC, for which feedback may enlarge maximum-error-probability capacity regions, but not average-error-capacity regions. Besides, we present a class of MAC, as an example for which the maximum-error-probability capacity regions are strictly smaller than the average-error-probability capacity regions (first example showing this was due to G. Dueck). Differently from G. Dueck’s enlightening example in which a deterministic MAC was considered, our example includes and further generalizes G. Dueck’s example by taking both deterministic and non-deterministic MACs into account. Finally, we extend our results for a discrete memoryless two-input channel, to compound, arbitrarily varying MAC, and MAC with more than two inputs.
Keywords: average/maximum probability of error; random/deterministic encoder; feedback; multiple input channel; Chernoff bound average/maximum probability of error; random/deterministic encoder; feedback; multiple input channel; Chernoff bound
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

Scifeed alert for new publications

Never miss any articles matching your research from any publisher
  • Get alerts for new papers matching your research
  • Find out the new papers from selected authors
  • Updated daily for 49'000+ journals and 6000+ publishers
  • Define your Scifeed now

SciFeed Share & Cite This Article

MDPI and ACS Style

Cai, N. The Maximum Error Probability Criterion, Random Encoder, and Feedback, in Multiple Input Channels. Entropy 2014, 16, 1211-1242.

Show more citation formats Show less citations formats

Related Articles

Article Metrics

Article Access Statistics

1

Comments

[Return to top]
Entropy EISSN 1099-4300 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top