Related papers: How to Quantize $n$ Outputs of a Binary Symmetric …
We study the most-informative Boolean function conjecture using a differential equation approach. This leads to a formulation of a functional inequality on finite-dimensional random variables. We also develop a similar inequality in the…
The Courtade-Kumar conjecture posits that dictatorship functions maximize the mutual information between the function's output and a noisy version of its input over the Boolean hypercube. We present two significant advancements related to…
This paper considers the problem of approximating a Boolean function $f$ using another Boolean function from a specified class. Two classes of approximating functions are considered: $k$-juntas, and linear Boolean functions. The $n$ input…
Consider a point-to-point communication system in which the transmitter holds a binary message of length $m$ and transmits a corresponding codeword of length $n$. The receiver's goal is to recover a Boolean function of that message, where…
We consider the Courtade-Kumar most informative Boolean function conjecture for balanced functions, as well as a conjecture by Li and M\'edard that dictatorship functions also maximize the $L^\alpha$ norm of $T_pf$ for $1\leq\alpha\leq2$…
In this paper, we investigate the quantization of the output of a binary input discrete memoryless channel that maximizing the mutual information between the input and the quantized output under an entropy-constrained of the quantized…
Classification of Non-linear Boolean functions is a long-standing problem in the area of theoretical computer science. In this paper, effort has been made to achieve a systematic classification of all n-variable Boolean functions, where…
In this paper, we establish a new bound tying together the effective length and the maximum correlation between the outputs of an arbitrary pair of Boolean functions which operate on two sequences of correlated random variables. We derive a…
The quantization of the output of a binary-input discrete memoryless channel to a smaller number of levels is considered. An algorithm which finds an optimal quantizer, in the sense of maximizing mutual information between the channel input…
For information transmission a binary symmetric channel is used. There is also another noisy binary symmetric channel (feedback channel), and the transmitter observes without delay all the outputs of the forward channel via that feedback…
We characterize the power of constant-depth Boolean circuits in generating uniform symmetric distributions. Let $f\colon\{0,1\}^m\to\{0,1\}^n$ be a Boolean function where each output bit of $f$ depends only on $O(1)$ input bits. Assume the…
What is the value of a single bit to a guesser? We study this problem in a setup where Alice wishes to guess an i.i.d. random vector, and can procure one bit of information from Bob, who observes this vector through a memoryless channel. We…
A major open problem in communication complexity is whether or not quantum protocols can be exponentially more efficient than classical protocols on _total_ Boolean functions in the two-party interactive model. The answer appears to be…
We consider the transmission of nonexponentially many messages through a binary symmetric channel with noiseless feedback. We obtain an upper bound for the best decoding error exponent. Combined with the corresponding known lower bound,…
We investigate the influences of variables on a Boolean function $f$ based on the quantum Bernstein-Vazirani algorithm. A previous paper (Floess et al. in Math. Struct. in Comp. Science 23: 386, 2013) has proved that if a $n$-variable…
This paper presents a method to detect and recognize symmetries in Boolean functions. The idea is to use information theoretic measures of Boolean functions to detect sub-space of possible symmetric variables. Coupled with the new…
The largest Hamming distance between a Boolean function in $n$ variables and the set of all affine Boolean functions in $n$ variables is known as the covering radius $\rho_n$ of the $[2^n,n+1]$ Reed-Muller code. This number determines how…
We study functions on the infinite-dimensional Hamming cube $\{-1,1\}^\infty$, in particular Boolean functions into $\{-1,1\}$, generalising results on analysis of Boolean functions on $\{-1,1\}^n$ for $n\in\mathbb{N}$. The notion of noise…
Polynomial threshold gates are basic processing units of an artificial neural network. When the input vectors are binary vectors, these gates correspond to Boolean functions and can be analyzed via their polynomial representations. In…
A model of quantum noisy channel with input encoding by a classical random vector is described. An equation of optimality is derived to determine a complete set of wave functions describing quantum decodings based on quasi-measurements…