Related papers: List Decoding Algorithm based on Voting in Groebne…
In this paper, we assume an error such that a single insertion occurs and then a single deletion occurs. Under such an error model, this paper provides a decoding algorithm for non-binary quantum codes constructed by Matsumoto and Hagiwara.
In this work, we consider the problem of efficient decoding of codes from insertions and deletions. Most of the known efficient codes are codes with synchronization strings which allow one to reduce the problem of decoding insertions and…
Permutation decoding is a process that utilizes the permutation automorphism group of a linear code to correct errors in received words. Given a received word, a set of automorphisms, called a PD set, moves errors out of the information…
List-decoding and list-recovery are important generalizations of unique decoding that received considerable attention over the years. However, the optimal trade-off among list-decoding (resp. list-recovery) radius, list size, and the code…
In distributed optimization problems, a technique called gradient coding, which involves replicating data points, has been used to mitigate the effect of straggling machines. Recent work has studied approximate gradient coding, which…
Today's massively-sized datasets have made it necessary to often perform computations on them in a distributed manner. In principle, a computational task is divided into subtasks which are distributed over a cluster operated by a…
We combine the work of Garg and Konemann, and Fleischer with ideas from dynamic graph algorithms to obtain faster (1-eps)-approximation schemes for various versions of the multicommodity flow problem. In particular, if eps is moderately…
Folded Reed-Solomon (FRS) codes are a well-studied family of codes, known for achieving list decoding capacity. In this work, we give improved deterministic and randomized algorithms for list decoding FRS codes of rate $R$ up to radius…
Practically good error-correcting codes should have good parameters and efficient decoding algorithms. Some algebraically defined good codes such as cyclic codes, Reed-Solomon codes, and Reed-Muller codes have nice decoding algorithms.…
We study certain combinatorial aspects of list-decoding, motivated by the exponential gap between the known upper bound (of $O(1/\gamma)$) and lower bound (of $\Omega_p(\log (1/\gamma))$) for the list-size needed to decode up to radius $p$…
We improve the running time of the general algorithmic technique known as Baker's approach (1994) on H-minor-free graphs from O(n^{f(|H|)}) to O(f(|H|) n^{O(1)}). The numerous applications include e.g. a 2-approximation for coloring and…
We propose a decoding method for the generalized algebraic geometry codes proposed by Xing et al. To show its practical usefulness, we give an example of generalized algebraic geometry codes of length 567 over F_8 whose numbers of…
Due to the speed limitation of the conventional bit-chosen strategy in the existing weighted bit flipping algorithms, a high-speed LDPC decoder cannot be realized. To solve this problem, we propose a fast weighted bit flipping (FWBF)…
An iterative algorithm is presented for soft-input-soft-output (SISO) decoding of Reed-Solomon (RS) codes. The proposed iterative algorithm uses the sum product algorithm (SPA) in conjunction with a binary parity check matrix of the RS…
We develop new list decoding algorithms for Tanner codes and distance-amplified codes based on bipartite spectral expanders. We show that proofs exhibiting lower bounds on the minimum distance of these codes can be used as certificates…
Decoders for quantum LDPC codes generally rely on solving a parity-check equation with Gaussian elimination, with the generalised union-find decoder performing this repeatedly on growing clusters. We present an online variant of the…
In this paper we describe a variation of the classical permutation decoding algorithm that can be applied to any affine-invariant code with respect to certain type of information sets. In particular, we can apply it to the family of…
Transducer models have emerged as a promising choice for end-to-end ASR systems, offering a balanced trade-off between recognition accuracy, streaming capabilities, and inference speed in greedy decoding. However, beam search significantly…
Short-length Reed--Muller codes under majority-logic decoding are of particular importance for efficient hardware implementations in real-time and embedded systems. This paper significantly improves Chen's two-step majority-logic decoding…
In addition to a proposed codeword, error correction decoders that provide blockwise soft output (SO) return an estimate of the likelihood that the decoding is correct. Following Forney, such estimates are traditionally only possible for…