Related papers: Advances in List Decoding of Polynomial Codes
Recursive decoding techniques are considered for Reed-Muller (RM) codes of growing length $n$ and fixed order $r.$ An algorithm is designed that has complexity of order $n\log n$ and corrects most error patterns of weight up to…
Despite their exceptional error-correcting properties, Reed-Solomon codes have been overlooked in distributed storage applications due to the common belief that they have poor repair bandwidth: A naive repair approach would require the…
Subspace codes were introduced in order to correct errors and erasures for randomized network coding, in the case where network topology is unknown (the noncoherent case). Subspace codes are indeed collections of subspaces of a certain…
When digital data are transmitted over a noisy channel, it is important to have a mechanism allowing recovery against a limited number of errors. Normally, a user string of 0's and 1's, called bits, is encoded by adding a number of…
In coding theory, Reed-Solomon codes are one of the most well-known and widely used classes of error-correcting codes. In this thesis we study and compare two major strategies known for their decoding procedure, the…
Power decoding, or "decoding using virtual interleaving" is a technique for decoding Reed--Solomon codes up to the Sudan radius. Since the method's inception, it has been an open question if it is possible to use this approach to decode up…
We propose efficient minimum-distance decoding and list-decoding algorithms for a certain class of analog subspace codes, referred to as character-polynomial (CP) codes, recently introduced by Soleymani and the second author. In particular,…
The Reed-Muller (RM) code encoding $n$-variate degree-$d$ polynomials over ${\mathbb F}_q$ for $d < q$, with its evaluation on ${\mathbb F}_q^n$, has relative distance $1-d/q$ and can be list decoded from a $1-O(\sqrt{d/q})$ fraction of…
Insertion and deletion (insdel for short) errors are synchronization errors in communication systems caused by the loss of positional information in the message. Reed-Solomon codes have gained a lot of interest due to its encoding…
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…
Polar codes have attracted much recent attention as the first codes with low computational complexity that provably achieve optimal rate-regions for a large class of information-theoretic problems. One significant drawback, however, is that…
This paper is concerned with list decoding of $2$-interleaved binary alternant codes. The principle of the proposed algorithm is based on a combination of a list decoding algorithm for (interleaved) Reed-Solomon codes and an algorithm for…
Reed-Muller codes are among the most important classes of locally correctable codes. Currently local decoding of Reed-Muller codes is based on decoding on lines or quadratic curves to recover one single coordinate. To recover multiple…
Regenerating codes provide an efficient way to recover data at failed nodes in distributed storage systems. It has been shown that regenerating codes can be designed to minimize the per-node storage (called MSR) or minimize the…
Error-correcting codes and related combinatorial constructs play an important role in several recent (and old) results in computational complexity theory. In this paper we survey results on locally-testable and locally-decodable…
A generalization of the Reiger bound is presented for the list decoding of burst errors. It is then shown that Reed-Solomon codes attain this bound.
A method for concatenating quantum error-correcting codes is presented. The method is applicable to a wide class of quantum error-correcting codes known as Calderbank-Shor-Steane (CSS) codes. As a result, codes that achieve a high rate in…
A scheme for concatenating the recently invented polar codes with non-binary MDS codes, as Reed-Solomon codes, is considered. By concatenating binary polar codes with interleaved Reed-Solomon codes, we prove that the proposed concatenation…
Lifted Reed-Solomon codes, a subclass of lifted affine-invariant codes, have been shown to be of high rate while preserving locality properties similar to generalized Reed-Muller codes, which they contain as subcodes. This work introduces a…
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…