Explicit Constructions of Two-Dimensional Reed-Solomon Codes in High Insertion and Deletion Noise Regime

09/08/2019
by   Shu Liu, et al.
0

Insertion and deletion (insdel for short) errors are synchronization errors in communication systems caused by the loss of positional information in the message. On top of its wide interest in its error correcting capability in the classical setting, Reed-Solomon codes also prove to have error correcting algorithms under insdel metric which is based on Guruswami-Sudan decoding algorithm. Despite this, there have been few studies on the insdel correcting capability of Reed-Solomon codes. Our contributions mainly consist of two parts. Firstly, we construct a family of 2-dimensional Reed-Solomon codes with insdel error correcting capability up to half its length. This result improves the insdel error correcting capability from the previous existing construction which was only logarithmic on the code length. Then, we provide an extension to the first construction to have insdel error correcting capability up to its length. In consequence, the asymptotic minimum insdel distance of our family achieves the upper bound provided by the Singleton bound. Furthermore, it provides an explicit family of Reed-Solomon codes which can be decodable against insdel errors up to its length.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
12/25/2020

Construction and Encoding Algorithm for Maximum Run-Length Limited Single Insertion/Deletion Correcting Code

Maximum run-length limited codes are constraint codes used in communicat...
research
06/01/2022

Strict Half-Singleton Bound, Strict Direct Upper Bound for Linear Insertion-Deletion Codes and Optimal Codes

Insertion-deletion codes (insdel codes for short) are used for correctin...
research
01/09/2019

Simple Codes and Sparse Recovery with Fast Decoding

Construction of error-correcting codes achieving a designated minimum di...
research
08/30/2018

Asymptotically Optimal Codes Correcting Fixed-Length Duplication Errors in DNA Storage Systems

A (tandem) duplication of length k is an insertion of an exact copy of...
research
05/05/2021

Improved Singleton bound on insertion-deletion codes and optimal constructions

Insertion-deletion codes (insdel codes for short) play an important role...
research
08/27/2021

Explicit Good Subspace-metric and Subset-metric Codes as Insertion-deletion Codes

In this paper motivated from subspace coding we introduce subspace-metri...
research
09/23/2019

Explicit and Efficient Constructions of Coding Schemes for the Binary Deletion Channel and the Poisson Repeat Channel

This work gives an explicit construction of a family of error correcting...

Please sign up or login with your details

Forgot password? Click here to reset