Related papers: Beyond Identification: Computing Boolean Functions…
This paper studies the important problem of quantum classification of Boolean functions from a entirely novel perspective. Typically, quantum classification algorithms allow us to classify functions with a probability of $1.0$, if we are…
A new channel coding approach was proposed in [1] for random multiple access communication over the discrete-time memoryless channel. The coding approach allows users to choose their communication rates independently without sharing the…
In the identification (ID) scheme proposed by Ahlswede and Dueck, the receiver's goal is simply to verify whether a specific message of interest was sent. Unlike Shannon's transmission codes, which aim for message decoding, ID codes for a…
This paper investigates the learnability of the nonlinearity property of Boolean functions using neural networks. We train encoder style deep neural networks to learn to predict the nonlinearity of Boolean functions from examples of…
Molecular communication (MC) enables information exchange at the nano- and microscale, with applications in areas like drug delivery and health monitoring. These event-driven scenarios often require alternatives to traditional transmission.…
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…
A group of transition probability functions form a Shannon's channel whereas a group of truth functions form a semantic channel. Label learning is to let semantic channels match Shannon's channels and label selection is to let Shannon's…
Boolean functions on the space $F_{2}^m$ are not only important in the theory of error-correcting codes, but also in cryptography, where they occur in private key systems. In these two cases, the nonlinearity of these function is a main…
We prove the Courtade-Kumar conjecture, which states that the mutual information between any Boolean function of an $n$-dimensional vector of independent and identically distributed inputs to a memoryless binary symmetric channel and the…
We present a powerful new loss function and training scheme for learning binary hash codes with any differentiable model and similarity function. Our loss function improves over prior methods by using log likelihood loss on top of an…
Feature hashing, also known as {\em the hashing trick}, introduced by Weinberger et al. (2009), is one of the key techniques used in scaling-up machine learning algorithms. Loosely speaking, feature hashing uses a random sparse projection…
In this manuscript, a general method for deriving filtering algorithms that involve a network of interconnected Bayesian filters is proposed. This method is based on the idea that the processing accomplished inside each of the Bayesian…
We consider the problem of communicating over a channel for which no mathematical model is specified, and the achievable rates are determined as a function of the channel input and output sequences known a-posteriori, without assuming any…
Capacity formulas and random-coding exponents are derived for a generalized family of Gel'fand-Pinsker coding problems. These exponents yield asymptotic upper bounds on the achievable log probability of error. In our model, information is…
The problem of blind identification of channel codes at a receiver involves identifying a code chosen by a transmitter from a known code-family, by observing the transmitted codewords through the channel. Most existing approaches for…
This paper examines the maximum code rate achievable by a data-driven communication system over some unknown discrete memoryless channel in the finite blocklength regime. A class of channel codes, called learning-based channel codes, is…
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…
The identification capacity is developed without randomization at neither the encoder nor the decoder. In particular, full characterization is established for the deterministic identification (DI) capacity for the Gaussian channel and for…
This paper proposes a novel semiotic framework for analyzing Large Language Models (LLMs), conceptualizing them as stochastic semiotic engines whose outputs demand active, asymmetric human interpretation. We formalize the trade-off between…
Ahlswede and Katona (1977) posed the following isodiametric problem in Hamming spaces: For every $n$ and $1\le M\le2^{n}$, determine the minimum average Hamming distance of binary codes with length $n$ and size $M$. Fu, Wei, and Yeung…