A complete characterization of minimax and maximin encoder-decoder policies for communication channels with incomplete statistical description
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.
- Publication:
-
NASA STI/Recon Technical Report A
- Pub Date:
- July 1985
- Bibcode:
- 1985STIA...8545593B
- Keywords:
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- Channel Noise;
- Communication Theory;
- Jamming;
- Maximum Principle;
- Minimax Technique;
- Saddle Points (Game Theory);
- Statistical Decision Theory;
- Coding;
- Decoding;
- Game Theory;
- Random Noise;
- Communications and Radar