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International Symposium on Information Theory and its Applications

4PSK coherent-state signals can be narrow sense group covariant with respect to F 4 by coding

Minami Tanaka, Asuka Ohashi, Tsuyoshi Sasaki Usuda

Published Oct 1, 2016• 0 citations
OpenAlex

Abstract

The formula of the channel matrix for group co-variant signals for classical-quantum communication has been studied to calculate the channel matrix analytically. However, despite its importance, the formula derived previously cannot be applied to coded q-ary phase shift keying (PSK) signals by linear codes over an extension field F q . To derive the formula for codes over F q , we focus on the 4PSK signals coded by the codes over F 4 . In the present paper, we propose a construction method of a code of length 2n over F 4 from a code of length n. If the original code is a group code, the coded 4PSK signals by the constructed code is narrow sense group covariant.

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The formula of the channel matrix for group co-variant signals for classical-quantum communication has been studied to calculate the channel matrix analytically. However, despite its importance, the formula derived previously cannot be applied to coded q-ary phase shift keying (PSK) signals by linear codes over an extension field F q . To derive the formula for codes over F q , we focus on the 4PSK signals coded by the codes over F 4 . In the present paper, we propose a construction method of a code of length 2n over F 4 from a code of length n. If the original code is a group code, the coded 4PSK signals by the constructed code is narrow sense group covariant.
The optimal distributions on a channel input that yield the random coding exponent, the expurgation exponent, and the zero-rate reliability function for a discrete classical-quantum channel with M-ary Phase Shift Keying (PSK) coherent state signal are analytically derived. In each case, the optimal distributions are given by a uniform distribution over the channel input alphabet. As a result, the expressions of the error exponents for M-ary PSK coherent state signal are simplified. By using this result, typical behavior of the error exponents is sketched in the case of M = 16.
The square-root measurement (SRM) is regarded as the optimum quantum measurement for symmetric signals and quasi-optimum measurements for any quantum signals. Therefore, deriving formulae for the channel matrix by using SRM is crucial in developing a theory of quantum communications. To date, formulae for these matrices are known for symmetric and group-covariant signals. However, there are important non-symmetric signals such as ASK, AMPM, and QAM signals, etc. In this paper, we demonstrate that the calculation of the channel matrix for 4m-ary AMPM signals can be simplified by using their partial symmetry.