Related papers: Statistical Decoding 2.0: Reducing Decoding to LPN
Prange's information set algorithm is a decoding algorithm for arbitrary linear codes. It decodes corrupted codewords of any $\mathbb{F}_2$-linear code $C$ of message length $n$ up to relative error rate $O(\log n / n)$ in…
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…
Post-quantum cryptography currently rests on a small number of hardness assumptions, posing significant risks should any one of them be compromised. This vulnerability motivates the search for new and cryptographically versatile assumptions…
Low Rank Parity Check (LRPC) codes form a class of rank-metric error-correcting codes that was purposely introduced to design public-key encryption schemes. An LRPC code is defined from a parity check matrix whose entries belong to a…
The LPN (Learning Parity with Noise) problem has recently proved to be of great importance in cryptology. A special and very useful case is the RING-LPN problem, which typically provides improved efficiency in the constructed cryptographic…
In this article we address the computational hardness of optimally decoding a quantum stabilizer code. Much like classical linear codes, errors are detected by measuring certain check operators which yield an error syndrome, and the…
Decoding quantum error-correcting codes is a key challenge in enabling fault-tolerant quantum computation. In the classical setting, linear programming (LP) decoders offer provable performance guarantees and can leverage fast practical…
Several recently proposed code-based cryptosystems base their security on a slightly generalized version of the classical (syndrome) decoding problem. Namely, in the so-called restricted (syndrome) decoding problem, the error values stem…
Quantum cryptography via key distribution mechanisms that utilize quantum entanglement between sender-receiver pairs will form the basis of future large-scale quantum networks. A key engineering challenge in such networks will be the…
We introduce a novel algorithm for decoding binary linear codes by linear programming. We build on the LP decoding algorithm of Feldman et al. and introduce a post-processing step that solves a second linear program that reweights the…
Maximum Likelihood (ML) decoding is the optimal decoding algorithm for arbitrary linear block codes and can be written as an Integer Programming (IP) problem. Feldman et al. relaxed this IP problem and presented Linear Programming (LP)…
While low-density parity-check (LDPC) codes are near capacity-achieving when paired with iterative decoders, these decoders may not output a codeword due to the existence of pseudocodewords. Thus, pseudocodewords have been studied to give…
Low-density parity-check codes, a class of capacity-approaching linear codes, are particularly recognized for their efficient decoding scheme. The decoding scheme, known as the sum-product, is an iterative algorithm consisting of passing…
In a digital communication system, information is sent from one place to another over a noisy communication channel. It may be possible to detect and correct errors that occur during the transmission if one encodes the original information…
Decoding algorithms are essential to fault-tolerant quantum-computing architectures. In this perspective we explore decoding algorithms for the surface code; a prototypical quantum low-density parity-check code that underlies many of the…
The concept of Generalized Inverse based Decoding (GID) is introduced, as an algebraic framework for the syndrome decoding problem (SDP) and low weight codeword problem (LWP). The framework has ground on two characterizations by generalized…
In Linear Programming (LP) decoding of a Low-Density-Parity-Check (LDPC) code one minimizes a linear functional, with coefficients related to log-likelihood ratios, over a relaxation of the polytope spanned by the codewords \cite{03FWK}. In…
The order statistics based list decoding techniques for linear binary block codes of small to medium block length are investigated. The construction of the list of the test error patterns is considered. The original order statistics…
The use of parity-check gates in information theory has proved to be very efficient. In particular, error correcting codes based on parity checks over low-density graphs show excellent performances. Another basic issue of information…
We propose a quantized decoding algorithm for low- density parity-check codes where the variable node update rule of the standard min-sum algorithm is replaced with a look-up table (LUT) that is designed using an information-theoretic…