Related papers: Redundancies of Correction-Capability-Optimized Re…

This paper presents several new construction techniques for low-density parity-check (LDPC) and systematic repeat-accumulate (RA) codes. Based on specific classes of combinatorial designs, the improved code design focuses on high-rate…

Large Language Models (LLMs) have demonstrated impressive capabilities in understanding and generating codes. Due to these capabilities, many recent methods are proposed to automatically refine the codes with LLMs. However, we should…

We propose a modified iterative bounded distance decoding of product codes. The proposed algorithm is based on exchanging hard messages iteratively and exploiting channel reliabilities to make hard decisions at each iteration. Performance…

The sequence reconstruction problem, introduced by Levenshtein in 2001, considers a communication setting in which a sender transmits a codeword and the receiver observes K independent noisy versions of this codeword. In this work, we study…

In the search for highly efficient decoders for short LDPC codes approaching maximum likelihood performance, a relayed decoding strategy, specifically activating the ordered statistics decoding process upon failure of a neural min-sum…

Despite Retrieval-Augmented Generation improving code completion, traditional retrieval methods struggle with information redundancy and a lack of diversity within limited context windows. To solve this, we propose a resource-optimized…

Improvements in the performance of computing systems, driven by Moore's Law, have transformed society. As such hardware-driven gains slow down, it becomes even more important for software developers to focus on performance and efficiency…

In this work we propose RELDEC, a novel approach for sequential decoding of moderate length low-density parity-check (LDPC) codes. The main idea behind RELDEC is that an optimized decoding policy is subsequently obtained via reinforcement…

We introduce the notion of fault-tolerant quantum metrology to overcome noise beyond our control -- associated with sensing the parameter, by reducing the noise in operations under our control -- associated with preparing and measuring…

We approach index coding as a special case of rate-distortion with multiple receivers, each with some side information about the source. Specifically, using techniques developed for the rate-distortion problem, we provide two upper bounds…

Modern neural machine translation (NMT) models employ a large number of parameters, which leads to serious over-parameterization and typically causes the underutilization of computational resources. In response to this problem, we…

We survey the known list decoding algorithms for polar codes and compare their complexity. Index terms: Polar codes; Reed-Muller codes; successive cancellation decoding.

Large Language Models (LLMs) have demonstrated impressive performance on multiple-choice question answering (MCQA) benchmarks, yet they remain highly vulnerable to minor input perturbations. In this paper, we introduce and evaluate Token…

For Reed-Solomon codes, the key equation relates the syndrome polynomial---computed from the parity check matrix and the received vector---to two unknown polynomials, the locator and the evaluator. The roots of the locator polynomial…

The performance of an error correcting code is evaluated by its error probability, rate, and en/decoding complexity. The performance of a series of codes is evaluated by, as the block lengths approach infinity, whether their error…

Codes for rank modulation have been recently proposed as a means of protecting flash memory devices from errors. We study basic coding theoretic problems for such codes, representing them as subsets of the set of permutations of $n$…

Ahlswede and Dueck identification has the potential of exponentially reducing traffic or exponentially increasing rates in applications where a full decoding of the message is not necessary and, instead, a simple verification of the message…

The analysis of the decoding failure rate of the bit-flipping algorithm has received increasing attention. For a binary linear code we consider the minimum number of rows in a parity-check matrix such that the bit-flipping algorithm is able…

In this paper, soft-decision (SD) decoders of permutation trellis code (PTC) with $M$-ary frequency shift keying are designed using three optimization algorithms and presented in four decoding schemes. In a concatenated code such as PTC,…

First- and second-order Reed-Muller (RM(1) and RM(2), respectively) codes are two fundamental error-correcting codes which arise in communication as well as in probabilistically-checkable proofs and learning. In this paper, we take the…