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Error correction codes are a crucial part of the physical communication layer, ensuring the reliable transfer of data over noisy channels. The design of optimal linear block codes capable of being efficiently decoded is of major concern,…
We are motivated by problems that arise in a number of applications such as Online Marketing and explosives detection, where the observations are usually modeled using Poisson statistics. We model each observation as a Poisson random…
In this paper, we study binary constrained codes that are resilient to bit-flip errors and erasures. In our first approach, we compute the sizes of constrained subcodes of linear codes. Since there exist well-known linear codes that achieve…
In this paper, we propose {\em distributed network compression via memory}. We consider two spatially separated sources with correlated unknown source parameters. We wish to study the universal compression of a sequence of length $n$ from…
The performance of maximum-likelihood (ML) decoded binary linear block codes is addressed via the derivation of tightened upper bounds on their decoding error probability. The upper bounds on the block and bit error probabilities are valid…
This work provides an algebraic framework for source coding with decoder side information and its dual problem, channel coding with encoder side information, showing that nested concatenated codes can achieve the corresponding…
In a {\em locally recoverable} or {\em repairable} code, any symbol of a codeword can be recovered by reading only a small (constant) number of other symbols. The notion of local recoverability is important in the area of distributed…
We consider universal variable-to-fixed length compression of memoryless sources with a fidelity criterion. We design a dictionary codebook over the reproduction alphabet which is used to parse the source stream. Once a source subsequence…
It has recently been observed that certain extremely simple feature encoding techniques are able to achieve state of the art performance on several standard image classification benchmarks including deep belief networks, convolutional nets,…
Consider two independent random strings having same length and taking values uniformly in a common finite alphabet. We study the order of the variance of the length of the longest common subsequences (LCS) of these strings when long blocks,…
This paper presents a novel information-theoretic perspective on generalization in machine learning by framing the learning problem within the context of lossy compression and applying finite blocklength analysis. In our approach, the…
A locally decodable code (LDC) C:{0,1}^k -> {0,1}^n is an error correcting code wherein individual bits of the message can be recovered by only querying a few bits of a noisy codeword. LDCs found a myriad of applications both in theory and…
String matching is the problem of deciding whether a given $n$-bit string contains a given $k$-bit pattern. We study the complexity of this problem in three settings. Communication complexity. For small $k$, we provide near-optimal upper…
We consider a distributed source coding system in which several observations are communicated to the decoder using limited transmission rate. The observations must be separately coded. We introduce a robust distributed coding scheme which…
Variable-length feedback coding has the potential to significantly enhance communication reliability in finite block length scenarios by adapting coding strategies based on real-time receiver feedback. Designing such codes, however, is…
In this paper, we present a new interpretation of non-negatively constrained convolutional coding problems as blind deconvolution problems with spatially variant point spread function. In this light, we propose an optimization framework…
A multi-user private data compression problem is studied. A server has access to a database of $N$ files, $(Y_1,...,Y_N)$, each of size $F$ bits and is connected to an encoder. The encoder is connected through an unsecured link to a user.…
The problem of variable length and fixed-distortion universal source coding (or D-semifaithful source coding) for stationary and memoryless sources on countably infinite alphabets ($\infty$-alphabets) is addressed in this paper. The main…
Polarization-adjusted convolutional (PAC) codes, as a concatenated coding scheme based on polar codes, is able to approach the finite-length bound of binary-input AWGN channel at short blocklengths. In this paper, we extend PAC codes to the…
Transformer architectures have achieved remarkable success across language, vision, and multimodal tasks, and there is growing demand for them to address in-context compositional learning tasks. In these tasks, models solve the target…