A Complete Characterization of Minimax and Maximin Encoder-Decoder Policies for Communication Channels with Incomplete Statistical Description

Tamer Basar, Ying Wah Wu

Research output: Contribution to journalArticlepeer-review

Abstract

The problem is considered of transmitting a sequence of independent and identically distributed Gaussian random variables over a channel whose statistical description is incomplete. The channel is modeled as one that is conditionally Gaussian, with the unknown part being controlled by a so-called “jammer” who may have access to the input to the encoder and operates under a given power constraint. By adopting a game-theoretic approach, a complete set of solutions is obtained (encoder and decoder mappings, and least-favorable distributions for the channel noise) for this statistical decision problem, under two different sets of conditions, depending on whether the encoder mapping is deterministic or stochastic. In the latter case, existence of a mixed saddle-point solution can be verified when a side channel of a specific nature is available between the transmitter and the receiver. In the former case, however, only minimax and maximin solutions can be derived.

Original languageEnglish (US)
Pages (from-to)482-489
Number of pages8
JournalIEEE Transactions on Information Theory
Volume31
Issue number4
DOIs
StatePublished - Jul 1985

ASJC Scopus subject areas

  • Information Systems
  • Computer Science Applications
  • Library and Information Sciences

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