Related papers: Families of Optimal Binary Non-MDS Erasure Codes
Convolutional codes are a class of error-correcting codes that performs very well over erasure channels with low delay requirements. In particular, Maximum Distance Profile (MDP) convolutional codes, which are defined to have optimal column…
Linear erasure codes with local repairability are desirable for distributed data storage systems. An [n, k, d] code having all-symbol (r, \delta})-locality, denoted as (r, {\delta})a, is considered optimal if it also meets the minimum…
In this paper, we mainly study quaternary linear codes and their binary subfield codes. First we obtain a general explicit relationship between quaternary linear codes and their binary subfield codes in terms of generator matrices and…
We investigate adaptive single-trial error/erasure decoding of binary codes whose decoder is able to correct e errors and t erasures if le+t<=d-1. Thereby, d is the minimum Hamming distance of the code and 1<l<=2 is the tradeoff parameter…
Folded Reed-Solomon codes are an explicit family of codes that achieve the optimal trade-off between rate and error-correction capability: specifically, for any $\eps > 0$, the author and Rudra (2006,08) presented an $n^{O(1/\eps)}$ time…
Reed-Solomon (RS) codes are an important class of non-binary error-correction codes. They are particularly competent in correcting burst errors, being widely applied in modern communications and data storage systems. This also thanks to…
We focus on erasure codes for distributed storage. The distributed storage setting imposes locality requirements because of easy repair demands on the decoder. We first establish the characterization of various locality properties in terms…
In this work we describe an efficient implementation of a hierarchy of algorithms for the decomposition of dense matrices over the field with two elements (GF(2)). Matrix decomposition is an essential building block for solving dense…
With the growth of image on the web, research on hashing which enables high-speed image retrieval has been actively studied. In recent years, various hashing methods based on deep neural networks have been proposed and achieved higher…
Codes for storage systems aim to minimize the repair locality, which is the number of disks (or nodes) that participate in the repair of a single failed disk. Simultaneously, the code must sustain a high rate, operate on a small finite…
A common problem on sequential-type decoding is that at the signal-to-noise ratio (SNR) below the one corresponding to the cutoff rate, the average decoding complexity per information bit and the required stack size grow rapidly with the…
The analysis of random coding error exponents pertaining to erasure/list decoding, due to Forney, is revisited. Instead of using Jensen's inequality as well as some other inequalities in the derivation, we demonstrate that an exponentially…
We present a simple deterministic reduction which, assuming the Exponential Time Hypothesis ($\mathsf{ETH}$), yields tight lower bounds for approximating the parameterized Maximum Likelihood Decoding problem ($\mathsf{MLD}$) and the…
Consider a binary maximum distance separable (MDS) array code composed of an $m\times (k+r)$ array of bits with $k$ information columns and $r$ parity columns, such that any $k$ out of $k+r$ columns suffice to reconstruct the $k$…
A class of two-bit bit flipping algorithms for decoding low-density parity-check codes over the binary symmetric channel was proposed in [1]. Initial results showed that decoders which employ a group of these algorithms operating in…
Hinging on ideas from physical-layer network coding, some promising proposals of coded random access systems seek to improve system performance (while preserving low complexity) by means of packet repetitions and decoding of linear…
We propose a bit-flip descent method for optimizing binary spreading codes with large family sizes and long lengths, addressing the challenges of large-scale code design in GNSS and emerging PNT applications. The method iteratively flips…
We introduce a class of bosonic quantum error-correcting codes, termed \emph{extended binomial codes}, which generalize the structure of one-mode binomial codes by incorporating ideas from high-rate qubit stabilizer codes. These codes are…
Lifted Reed-Solomon codes are a natural affine-invariant family of error-correcting codes which generalize Reed-Muller codes. They were known to have efficient local-testing and local-decoding algorithms (comparable to the known algorithms…
New algorithms for efficient decoding of polar codes (which may be CRC-augmented), transmitted over either a binary erasure channel (BEC) or an additive white Gaussian noise channel (AWGNC), are presented. We start by presenting a new…