TY - GEN

T1 - Erasure/list random coding error exponents are not universally achievable

AU - Weinberger, Nir

AU - Huleihel, Wasim

AU - Merhav, Neri

N1 - Publisher Copyright:
© 2015 IEEE.

PY - 2015/6/24

Y1 - 2015/6/24

N2 - We study the problem of universal decoding for unknown discrete memoryless channels in the presence of erasure/list option at the decoder, in the random coding regime. Specifically, we harness a universal version of Forney's classical erasure/list decoder developed in earlier studies, which is based on the competitive minimax methodology, and guarantees universal achievability of a certain fraction of the optimum random coding error exponents. In this paper, we derive an exact single-letter expression for the maximum achievable fraction. Examples are given in which the maximal achievable fraction is strictly less than unity, which imply that, in general, there is no universal erasure/list decoder which achieves the same random coding error exponents as the optimal decoder for a known channel. This is in contrast to the situation in ordinary decoding (without the erasure/list option), where optimum exponents are universally achievable, as is well known. It is also demonstrated that previous lower bounds derived for the maximal achievable fraction are not tight in general.

AB - We study the problem of universal decoding for unknown discrete memoryless channels in the presence of erasure/list option at the decoder, in the random coding regime. Specifically, we harness a universal version of Forney's classical erasure/list decoder developed in earlier studies, which is based on the competitive minimax methodology, and guarantees universal achievability of a certain fraction of the optimum random coding error exponents. In this paper, we derive an exact single-letter expression for the maximum achievable fraction. Examples are given in which the maximal achievable fraction is strictly less than unity, which imply that, in general, there is no universal erasure/list decoder which achieves the same random coding error exponents as the optimal decoder for a known channel. This is in contrast to the situation in ordinary decoding (without the erasure/list option), where optimum exponents are universally achievable, as is well known. It is also demonstrated that previous lower bounds derived for the maximal achievable fraction are not tight in general.

UR - http://www.scopus.com/inward/record.url?scp=84938929412&partnerID=8YFLogxK

U2 - 10.1109/ITW.2015.7133083

DO - 10.1109/ITW.2015.7133083

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AN - SCOPUS:84938929412

T3 - 2015 IEEE Information Theory Workshop, ITW 2015

BT - 2015 IEEE Information Theory Workshop, ITW 2015

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 2015 IEEE Information Theory Workshop, ITW 2015

Y2 - 26 April 2015 through 1 May 2015

ER -