On MMSE properties of 'good' and 'bad' codes for the Gaussian broadcast channel

Ronit Bustin, Rafael F. Schaefer, H. Vincent Poor, Shlomo Shamai

Research output: Chapter in Book/Report/Conference proceedingConference contribution

3 Scopus citations

Abstract

This work examines the properties of code sequences for the scalar Gaussian broadcast channel (BC). Specifically, the behavior in terms of the mutual information and minimum mean-square error (MMSE) functions for all signal-to-noise ratios (SNRs) is explored. It is shown that 'good', capacity achieving, code sequences must follow the behavior of a capacity achieving superposition code sequence, even if they use a different encoding-decoding scheme (such as 'Dirty Paper Coding'). Necessary and sufficient conditions for reliable decoding in general and specifically for 'good' code sequences for the scalar Gaussian BC, in terms of the MMSE and conditional MMSE functions, are derived. Finally, 'bad' code sequences, that do not obtain the capacity of the scalar Gaussian BC, are examined. These codes are defined by an additional MMSE constraint at some other SNR. This constraint limits the amount of disturbance these codes may have on some unintended receiver at that SNR. The capacity region, given this constraint, is fully depicted.

Original languageEnglish (US)
Title of host publicationProceedings - 2015 IEEE International Symposium on Information Theory, ISIT 2015
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages391-395
Number of pages5
ISBN (Electronic)9781467377041
DOIs
StatePublished - Sep 28 2015
EventIEEE International Symposium on Information Theory, ISIT 2015 - Hong Kong, Hong Kong
Duration: Jun 14 2015Jun 19 2015

Publication series

NameIEEE International Symposium on Information Theory - Proceedings
Volume2015-June
ISSN (Print)2157-8095

Other

OtherIEEE International Symposium on Information Theory, ISIT 2015
CountryHong Kong
CityHong Kong
Period6/14/156/19/15

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Information Systems
  • Modeling and Simulation
  • Applied Mathematics

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