TY - GEN

T1 - On the calculation of the minimax-converse of the channel coding problem

AU - Elkayam, Nir

AU - Feder, Meir

N1 - Publisher Copyright:
© 2017 IEEE.

PY - 2017/8/9

Y1 - 2017/8/9

N2 - A minimax-converse has been suggested for the general channel coding problem [1]. This converse comes in two flavors. The first flavor is generally used for the analysis of the coding problem with non-vanishing error probability and provides an upper bound on the rate given the error probability. The second flavor fixes the rate and provides a lower bound on the error probability. Both converses are given as a min-max optimization problem of an appropriate binary hypothesis testing problem. The properties of the first converse were studies in [2] and a saddle point was proved. The minimax solution can also be used in conjunction with random coding to achieve 'optimal' [3] coding performance. In this paper we study the properties of the second form, i.e. when the rate is fixed. Necessary and sufficient conditions on the saddle point solution are proved. Moreover, an algorithm for the computation of the saddle point, and hence the bound, is developed. In the DMC case, the algorithm runs in a polynomial time.

AB - A minimax-converse has been suggested for the general channel coding problem [1]. This converse comes in two flavors. The first flavor is generally used for the analysis of the coding problem with non-vanishing error probability and provides an upper bound on the rate given the error probability. The second flavor fixes the rate and provides a lower bound on the error probability. Both converses are given as a min-max optimization problem of an appropriate binary hypothesis testing problem. The properties of the first converse were studies in [2] and a saddle point was proved. The minimax solution can also be used in conjunction with random coding to achieve 'optimal' [3] coding performance. In this paper we study the properties of the second form, i.e. when the rate is fixed. Necessary and sufficient conditions on the saddle point solution are proved. Moreover, an algorithm for the computation of the saddle point, and hence the bound, is developed. In the DMC case, the algorithm runs in a polynomial time.

UR - http://www.scopus.com/inward/record.url?scp=85034039362&partnerID=8YFLogxK

U2 - 10.1109/ISIT.2017.8006728

DO - 10.1109/ISIT.2017.8006728

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AN - SCOPUS:85034039362

T3 - IEEE International Symposium on Information Theory - Proceedings

SP - 1247

EP - 1251

BT - 2017 IEEE International Symposium on Information Theory, ISIT 2017

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 2017 IEEE International Symposium on Information Theory, ISIT 2017

Y2 - 25 June 2017 through 30 June 2017

ER -