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I will show that there is a deep relation between error-correction codes and certain mathematical models of spin glasses. In particular minimum error probability decoding is equivalent to finding the ground state of the corresponding spin…
Reed-Muller (RM) codes are known for their good maximum likelihood (ML) performance in the short block-length regime. Despite being one of the oldest classes of channel codes, finding a low complexity soft-input decoding scheme is still an…
Complex statistical models are often built by combining multiple submodels, called modules. Here we consider modular inference where the modules contain both parametric and nonparametric components. In such cases, standard Bayesian…
We consider the problem of coded distributed computing where a large linear computational job, such as a matrix multiplication, is divided into $k$ smaller tasks, encoded using an $(n,k)$ linear code, and performed over $n$ distributed…
Reed-Solomon (RS) codes are widely used to correct errors in storage systems. Finding the error locator polynomial is one of the key steps in the error correction procedure of RS codes. Modular Approach (MA) is an effective algorithm for…
While a mature body of work supports the study of rewriting systems, abstract tools for Probabilistic Rewriting are still limited. In this paper we study the question of uniqueness of the result (unique limit distribution), and develop a…
This paper is concerned with list decoding of $2$-interleaved binary alternant codes. The principle of the proposed algorithm is based on a combination of a list decoding algorithm for (interleaved) Reed-Solomon codes and an algorithm for…
We speed up existing decoding algorithms for three code classes in different metrics: interleaved Gabidulin codes in the rank metric, lifted interleaved Gabidulin codes in the subspace metric, and linearized Reed-Solomon codes in the…
This paper proposes a simple approach to derive efficient error bounds for learning multiple components with sparsity-inducing regularization. We show that for such regularization schemes, known decompositions of the Rademacher complexity…
The penalty incurred by imposing a finite delay constraint in lossless source coding of a memoryless source is investigated. It is well known that for the so-called block-to-variable and variable-to-variable codes, the redundancy decays at…
We propose a list-decoding scheme for reconstruction codes in the context of uniform-tandem-duplication noise, which can be viewed as an application of the associative memory model to this setting. We find the uncertainty associated with…
We consider a novel variant of $d$-semifaithful lossy coding in which the distortion measure is revealed only to the encoder and only at run-time, as well as an extension of it in which the distortion constraint $d$ is also revealed at…
Recent theoretical developments in coset coding theory have provided continuous-valued functions which give the equivocation and maximum likelihood (ML) decoding probability of coset secrecy codes. In this work, we develop a method for…
This paper aims to delve into the rate-distortion-complexity trade-offs of modern neural video coding. Recent years have witnessed much research effort being focused on exploring the full potential of neural video coding. Conditional…
In this paper, a new approach for decoding low-rate Reed-Solomon codes beyond half the minimum distance is considered and analyzed. Unlike the Sudan algorithm published in 1997, this new approach is based on multi-sequence shift-register…
We solve a problem due to Recam\'an about the lower bound behavior of the maximum possible length among all arithmetic progressions in the least reduced residue system modulo $n$, as $n \to \infty$.
The residual vector quantization (RVQ) technique plays a central role in recent advances in neural audio codecs. These models effectively synthesize high-fidelity audio from a limited number of codes due to the hierarchical structure among…
We propose a slight modification of the Berlekamp-Massey Algorithm for obtaining the minimal polynomial of a given linearly recurrent sequence. Such a modification enables to explain it in a simpler way and to adapt it to lazy evaluation.
We decode Reed-Solomon codes using soft information provided at the receiver. The Extended Euclidean Algorithm (EEA) is considered as an initial step to obtain an intermediate result. The final decoding result is obtained by interpolating…
Recently, the authors showed that Reed-Muller (RM) codes achieve capacity on binary memoryless symmetric (BMS) channels with respect to bit error rate. This paper extends that work by showing that RM codes defined on non-binary fields,…