On the error probability of stochastic decision and stochastic decoding
Abstract
This paper investigates the error probability of a stochastic decision and the way in which it differs from the error probability of an optimal decision, i.e., the maximum a posteriori decision. This paper calls attention to the fact that the error probability of a stochastic decision with the a posteriori distribution is at most twice the error probability of the maximum a posteriori decision. It is shown that, by generating an independent identically distributed random sequence subject to the a posteriori distribution and making a decision that maximizes the a posteriori probability over the sequence, the error probability approaches exponentially the error probability of the maximum a posteriori decision as the sequence length increases. Using these ideas as a basis, we can construct stochastic decoders for source/channel codes.
Cite
@article{arxiv.1701.04950,
title = {On the error probability of stochastic decision and stochastic decoding},
author = {Jun Muramatsu and Shigeki Miyake},
journal= {arXiv preprint arXiv:1701.04950},
year = {2017}
}
Comments
(v1) 10 pages. This is the extended version of the paper submitted to ISIT2017. (v2) References for Theorem 1 are added. (v3) submitted to IEEE Transactions on Information Theory