Related papers: List and Probabilistic Unique Decoding of Folded S…
This paper studies random-coding error exponents of randomised list decoding, in which the decoder randomly selects $L$ messages with probabilities proportional to the decoding metric of the codewords. The exponents (or bounds) are given…
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…
The code that combines channel estimation and error protection has received general attention recently, and has been considered a promising methodology to compensate multi-path fading effect. It has been shown by simulations that such code…
Multivariate multiplicity codes (Kopparty, Saraf, and Yekhanin, J. ACM 2014) are linear codes where the codewords are described by evaluations of multivariate polynomials (with a degree bound) and their derivatives up to a fixed order, on a…
We consider recursive decoding techniques for RM codes, their subcodes, and newly designed codes. For moderate lengths up to 512, we obtain near-optimum decoding with feasible complexity.
We present algorithms performing sparse univariate polynomial interpolation with errors in the evaluations of the polynomial. Based on the initial work by Comer, Kaltofen and Pernet [Proc. ISSAC 2012], we define the sparse polynomial…
In this paper motivated from subspace coding we introduce subspace-metric codes and subset-metric codes. These are coordinate-position independent pseudometrics and suitable for the folded codes. The half-Singleton upper bounds for linear…
Erasure list decoding was introduced to correct a larger number of erasures with output of a list of possible candidates. In the present paper, we consider both random linear codes and algebraic geometry codes for list decoding erasure…
In this paper we study spread codes: a family of constant-dimension codes for random linear network coding. In other words, the codewords are full-rank matrices of size (k x n) with entries in a finite field F_q. Spread codes are a family…
Tensor codes are a generalisation of matrix codes. Such codes are defined as subspaces of order-r tensors for which the ambient space is endowed with the tensor-rank as a metric. A class of these codes was introduced by Roth, who also…
Undetected errors are important for linear codes, which are the only type of errors after hard decision and automatic-repeat-request (ARQ), but do not receive much attention on their correction. In concatenated channel coding, suboptimal…
We describe a new class of list decodable codes based on Galois extensions of function fields and present a list decoding algorithm. These codes are obtained as a result of folding the set of rational places of a function field using…
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…
Color codes are a class of topological quantum codes with a high error threshold and large set of transversal encoded gates, and are thus suitable for fault tolerant quantum computation in two-dimensional architectures. Recently,…
Many probabilistic inference tasks involve summations over exponentially large sets. Recently, it has been shown that these problems can be reduced to solving a polynomial number of MAP inference queries for a model augmented with randomly…
This paper introduces a new counting code. Its design was motivated by distributed video coding where, for decoding, error correction methods are applied to improve predictions. Those error corrections sometimes fail which results in…
Consider a distributed coding for computing problem with constant decoding locality, i.e., with a vanishing error probability, any single sample of the function can be approximately recovered by probing only constant number of compressed…
Practical random network coding based schemes for multicast include a header in each packet that records the transformation between the sources and the terminal. The header introduces an overhead that can be significant in certain…
In this work, we present an abstract framework for some algebraic error-correcting codes with the aim of capturing codes that are list-decodable to capacity, along with their decoding algorithm. In the polynomial ideal framework, a code is…
Sparse random linear network coding (SRLNC) used as a class of erasure codes to ensure the reliability of multicast communications has been widely investigated. However, an exact expression for the decoding success probability of SRLNC is…