Related papers: A new method for erasure decoding of convolutional…
Concurrent coding is an encoding scheme with "holographic" type properties that are shown here to be robust against a significant amount of noise and signal loss. This single encoding scheme is able to correct for random errors and burst…
Deep neural network models have a complex architecture and are overparameterized. The number of parameters is more than the whole dataset, which is highly resource-consuming. This complicates their application and limits its usage on…
In this paper, we study the problem of storing an archive of versioned data in a reliable and efficient manner in distributed storage systems. We propose a new storage technique called differential erasure coding (DEC) where the differences…
This paper considers the problem of implementing large-scale gradient descent algorithms in a distributed computing setting in the presence of {\em straggling} processors. To mitigate the effect of the stragglers, it has been previously…
Due to the recent challenges in post-quantum cryptography, several new approaches for code-based cryptography have been proposed. For example, a variant of the McEliece cryptosystem based on interleaved codes was proposed. In order to deem…
In this paper, we present an analytical analysis of the convergence of raptor codes under joint decoding over the binary input additive white noise channel (BIAWGNC), and derive an optimization method. We use Information Content evolution…
This paper introduces an algorithm designed to approximate quantum transformation matrix with a restricted number of gates by using the block decomposition technique. Addressing challenges posed by numerous gates in handling large qubit…
Distributed matrix multiplication is widely used in several scientific domains. It is well recognized that computation times on distributed clusters are often dominated by the slowest workers (called stragglers). Recent work has…
We present a theory of quantum serial turbo-codes, describe their iterative decoding algorithm, and study their performances numerically on a depolarization channel. Our construction offers several advantages over quantum LDPC codes. First,…
In this paper, a novel decoding algorithm for low-density parity-check (LDPC) codes based on convex optimization is presented. The decoding algorithm, called interior point decoding, is designed for linear vector channels. The linear vector…
We consider binary systematic network codes and investigate their capability of decoding a source message either in full or in part. We carry out a probability analysis, derive closed-form expressions for the decoding probability and show…
We describe a successive-cancellation \emph{list} decoder for polar codes, which is a generalization of the classic successive-cancellation decoder of Ar{\i}kan. In the proposed list decoder, up to $L$ decoding paths are considered…
We consider recursive decoding for Reed-Muller (RM) codes and their subcodes. Two new recursive techniques are described. We analyze asymptotic properties of these algorithms and show that they substantially outperform other decoding…
We introduce a quantum Maxwell erasure decoder for CSS quantum low-density parity-check (qLDPC) codes that extends peeling with bounded guessing. Guesses are tracked symbolically and can be eliminated by restrictive checks, giving a tunable…
Recent developments in the field of deep learning have motivated many researchers to apply these methods to problems in quantum information. Torlai and Melko first proposed a decoder for surface codes based on neural networks. Since then,…
Quantum low-density parity-check (qLDPC) codes are promising for realizing scalable fault-tolerant quantum computation due to their potential for low-overhead protocols. A common approach to decoding qLDPC codes is to use the belief…
We introduce a new method for decoding short and moderate length linear block codes with dense parity-check matrix representations of cyclic form, termed multiple-bases belief-propagation (MBBP). The proposed iterative scheme makes use of…
The interesting properties of classical Goppa code and its effective decoding algorithm (algorithm of patterson) make the most appropriate candidate for use in the MC Eliece cryptosystem. Information leakage which results from the…
In this paper we present a new class of convolutional codes that admits an efficient al- gebraic decoding algorithm. We study some of its properties and show that it can decode interesting sequences of errors patterns. The second part of…
We propose an efficient encoding algorithm for the binary and non-binary low-density parity-check codes. This algorithm transforms the parity part of the parity-check matrix into a block triangular matrix with low weight diagonal…