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- W4297067239 abstract "Suppose that $Y^n$ is obtained by observing a uniform Bernoulli random vector $X^n$ through a binary symmetric channel with crossover probability $alpha$. The most informative Boolean function conjecture postulates that the maximal mutual information between $Y^n$ and any Boolean function $mathrm{b}(X^n)$ is attained by a dictator function. In this paper, we consider the complementary case in which the Boolean function is replaced by $f:left{0,1right}^ntoleft{0,1right}^{n-1}$, namely, an $n-1$ bit quantizer, and show that $I(f(X^n);Y^n)leq (n-1)cdotleft(1-h(alpha)right)$ for any such $f$. Thus, in this case, the optimal function is of the form $f(x^n)=(x_1,ldots,x_{n-1})$." @default.
- W4297067239 created "2022-09-26" @default.
- W4297067239 creator A5004351362 @default.
- W4297067239 creator A5043037048 @default.
- W4297067239 date "2017-01-11" @default.
- W4297067239 modified "2023-10-16" @default.
- W4297067239 title "How to Quantize $n$ Outputs of a Binary Symmetric Channel to $n-1$ Bits?" @default.
- W4297067239 doi "https://doi.org/10.48550/arxiv.1701.03119" @default.
- W4297067239 hasPublicationYear "2017" @default.
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