Related papers: Fast Decoding of Interleaved Linearized Reed-Solom…
This paper shows that there exist Reed--Solomon (RS) codes, over \black{exponentially} large finite fields \black{in the code length}, that are combinatorially list-decodable well beyond the Johnson radius, in fact almost achieving the…
Reed-Muller (RM) and polar codes are a class of capacity-achieving channel coding schemes with the same factor graph representation. Low-complexity decoding algorithms fall short in providing a good error-correction performance for RM and…
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…
List-decoding of Reed-Solomon (RS) codes beyond the so called Johnson radius has been one of the main open questions since the work of Guruswami and Sudan. It is now known by the work of Rudra and Wootters, using techniques from high…
Lifted Reed-Solomon and multiplicity codes are classes of codes, constructed from specific sets of $m$-variate polynomials. These codes allow for the design of high-rate codes that can recover every codeword or information symbol from many…
The paper introduces the simultaneous partial-inverse problem (SPI) for polynomials and develops its application to decoding interleaved Reed--Solomon codes beyond half the minimum distance. While closely related both to standard key…
MDS codes play a central role in practice due to their broad applications. To date, most known MDS codes are generalized Reed-Solomon (GRS) codes, leaving codes that are not equivalent to GRS codes comparatively less understood. Studying…
Generalized Reed-Solomon (GRS) and Gabidulin codes have been proposed for various code-based cryptosystems, though most such schemes without elaborate disguising techniques have been successfully attacked. Both code classes are prominent…
Because of their importance in applications and their quite simple definition, Reed-Solomon codes can be explained in any introductory course on coding theory. However, decoding algorithms for Reed-Solomon codes are far from being simple…
We examine regular and irregular repeat-accumulate (RA) codes with repetition degrees which are all even. For these codes and with a particular choice of an interleaver, we give an upper bound on the decoding error probability of a…
We propose to reduce the decoding complexity of polar codes with non-Arikan kernels by employing a (near) ML decoding algorithm for the codes generated by kernel rows. A generalization of the order statistics algorithm is presented for soft…
Skew polynomials are a class of non-commutative polynomials that have several applications in computer science, coding theory and cryptography. In particular, skew polynomials can be used to construct and decode evaluation codes in several…
Algorithms based on multiple decoding attempts of Reed-Solomon (RS) codes have recently attracted new attention. Choosing decoding candidates based on rate-distortion (R-D) theory, as proposed previously by the authors, currently provides…
Guo, Kopparty and Sudan have initiated the study of error-correcting codes derived by lifting of affine-invariant codes. Lifted Reed-Solomon (RS) codes are defined as the evaluation of polynomials in a vector space over a field by requiring…
One popular approach to soft-decision decoding of Reed-Solomon (RS) codes is based on using multiple trials of a simple RS decoding algorithm in combination with erasing or flipping a set of symbols or bits in each trial. This paper…
In modern practical data centers, storage nodes are usually organized into equally sized groups, which is called racks. The cost of cross-rack communication is much more expensive compared with the intra-rack communication cost. The codes…
Starting from a practical use of Reed-Solomon codes in a cryptographic scheme published in Indocrypt'09, this paper deals with the threshold of linear $q$-ary error-correcting codes. The security of this scheme is based on the…
Power decoding, or "decoding by virtual interleaving", of Reed--Solomon codes is a method for unique decoding beyond half the minimum distance. We give a new variant of the Power decoding scheme, building upon the key equation of Gao. We…
Coding for distributed storage gives rise to a new set of problems in coding theory related to the need of reducing inter-node communication in the system. A large number of recent papers addressed the problem of optimizing the total amount…
This dissertation considers new constructions and decoding approaches for error-correcting codes based on non-conventional polynomials, with the objective of providing new coding solutions to the applications mentioned above. With skew…