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The growing gap between the increasing complexity of large language models (LLMs) and the limited computational budgets of edge devices poses a key challenge for efficient on-device inference, despite gradual improvements in hardware…

We explore the use of FCNNs (Fully Connected Neural Networks) for designing end-to-end communication systems without taking any inspiration from existing classical communications models or error control coding. This work relies solely on…

Sparse random linear network coding (SRLNC) is an attractive technique proposed in the literature to reduce the decoding complexity of random linear network coding. Recognizing the fact that the existing SRLNC schemes are not efficient in…

The development of practical, high-performance decoding algorithms reduces the resource cost of fault-tolerant quantum computing. Here we propose a decoder for the surface code that finds low-weight correction operators for errors produced…

In decoding linear block codes, it was shown that noticeable reliability gains can be achieved by introducing learnable parameters to the Belief Propagation (BP) decoder. Despite the success of these methods, there are two key open…

Concatenated bit-interleaved and multilevel coded modulation with outer Reed--Solomon codes, inner Chase-algorithm-based soft-decision-decoded Bose--Ray-Chaudhuri--Hocquenghem codes, and four-level pulse amplitude modulation is considered.…

A primary source of increased read time on NAND flash comes from the fact that in the presence of noise, the flash medium must be read several times using different read threshold voltages for the decoder to succeed. This paper proposes an…

Low-depth random circuit codes possess many desirable properties for quantum error correction but have so far only been analyzed in the code capacity setting where it is assumed that encoding gates and syndrome measurements are noiseless.…

Coding theory is a central discipline underpinning wireline and wireless modems that are the workhorses of the information age. Progress in coding theory is largely driven by individual human ingenuity with sporadic breakthroughs over the…

Typical random codes (TRC) in a communication scenario of source coding with side information at the decoder is the main subject of this work. We study the semi-deterministic code ensemble, which is a certain variant of the ordinary random…

We consider the problem of optimally decoding a quantum error correction code -- that is to find the optimal recovery procedure given the outcomes of partial "check" measurements on the system. In general, this problem is NP-hard. However,…

We present a framework that can exploit the tradeoff between the undetected error rate (UER) and block error rate (BLER) of polar-like codes. It is compatible with all successive cancellation (SC)-based decoding methods and relies on a…

Sparse superposition (SS) codes were originally proposed as a capacity-achieving communication scheme over the additive white Gaussian noise channel (AWGNC) [1]. Very recently, it was discovered that these codes are universal, in the sense…

We show that a simple modification of the surface code can exhibit an enormous gain in the error correction threshold for a noise model in which Pauli Z errors occur more frequently than X or Y errors. Such biased noise, where dephasing…

Starting from Shannon's celebrated 1948 channel coding theorem, we trace the evolution of channel coding from Hamming codes to capacity-approaching codes. We focus on the contributions that have led to the most significant improvements in…

Using techniques and results from Kudekar et al. we strengthen the bounds on the weight distribution of linear codes achieving capacity on the BEC, which were shown by the first author. In particular, we show that for any doubly transitive…

We propose a new class of efficient decoding algorithms for Reed-Muller (RM) codes over binary-input memoryless channels. The algorithms are based on projecting the code on its cosets, recursively decoding the projected codes (which are…

Large Language Models (LLMs) are increasingly applied to complex tasks that require extended reasoning. In such settings, models often benefit from diverse chains-of-thought to arrive at multiple candidate solutions. This requires two…

We construct pseudorandom error-correcting codes (or simply pseudorandom codes), which are error-correcting codes with the property that any polynomial number of codewords are pseudorandom to any computationally-bounded adversary. Efficient…

We consider the weighted belief-propagation (WBP) decoder recently proposed by Nachmani et al. where different weights are introduced for each Tanner graph edge and optimized using machine learning techniques. Our focus is on simple-scaling…