TY - GEN

T1 - How to quantize n outputs of a binary symmetric channel to n - 1 bits?

AU - Huleihel, Wasim

AU - Ordentlich, Or

N1 - Publisher Copyright:
© 2017 IEEE.

PY - 2017/8/9

Y1 - 2017/8/9

N2 - Suppose that Yn is obtained by observing a uniform Bernoulli random vector Xn through a binary symmetric channel with crossover probability α. The "most informative Boolean function" conjecture postulates that the maximal mutual information between Yn and any Boolean function b(Xn) is attained by a dictator function. In this paper, we consider the "complementary" case in which the Boolean function is replaced by f: {0, 1}n → {0,1}n, namely, an n - 1 bit quantizer, and show that I(f(Xn);Yn) < (n - 1) • (1 - h(α)) for any such f. Thus, in this case, the optimal function is of the form f(xn) = (x1,...,xn-1).

AB - Suppose that Yn is obtained by observing a uniform Bernoulli random vector Xn through a binary symmetric channel with crossover probability α. The "most informative Boolean function" conjecture postulates that the maximal mutual information between Yn and any Boolean function b(Xn) is attained by a dictator function. In this paper, we consider the "complementary" case in which the Boolean function is replaced by f: {0, 1}n → {0,1}n, namely, an n - 1 bit quantizer, and show that I(f(Xn);Yn) < (n - 1) • (1 - h(α)) for any such f. Thus, in this case, the optimal function is of the form f(xn) = (x1,...,xn-1).

UR - http://www.scopus.com/inward/record.url?scp=85034019203&partnerID=8YFLogxK

U2 - 10.1109/ISIT.2017.8006496

DO - 10.1109/ISIT.2017.8006496

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AN - SCOPUS:85034019203

T3 - IEEE International Symposium on Information Theory - Proceedings

SP - 91

EP - 95

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 -