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A Single-Letter Upper Bound to the Mismatch Capacity

Accepted version
Peer-reviewed

Type

Article

Change log

Authors

Asadi Kangarshahi, E  ORCID logo  https://orcid.org/0000-0002-7126-7007
Guillén I Fàbregas, A  ORCID logo  https://orcid.org/0000-0003-2795-1124

Abstract

We derive a single-letter upper bound to the mismatched-decoding capacity for discrete memoryless channels. The bound is expressed as the mutual information of a transformation of the channel, such that a maximum-likelihood decoding error on the translated channel implies a mismatched-decoding error in the original channel. In particular, a strong converse is shown to hold for this upper-bound: if the rate exceeds the upper-bound, the probability of error tends to 1 exponentially when the block-length tends to infinity. We also show that the underlying optimization problem is a convex-concave problem and that an efficient iterative algorithm converges to the optimal solution. In addition, we show that, unlike achievable rates in the literature, the multiletter version of the bound does not improve. A number of examples are discussed throughout the paper.

Description

Keywords

Maximum likelihood decoding, Channel estimation, Measurement, Error probability, Upper bound, Maximum likelihood estimation, Encoding, d-decoder, d-capacity, mismatch, shannon capacity, channel capacity, decoding

Journal Title

IEEE Transactions on Information Theory

Conference Name

Journal ISSN

0018-9448
1557-9654

Volume Title

67

Publisher

Institute of Electrical and Electronics Engineers (IEEE)

Rights

All rights reserved
Sponsorship
European Research Council (725411)
European Research Council under Grant 725411, and by the Spanish Ministry of Economy and Competitiveness under Grant TEC2016-78434-C3-1-R.