New Error Correcting Codes for Informed Receivers

TL;DR

This paper introduces new algebraic error correcting codes designed for scenarios where the receiver has prior knowledge of some messages, enabling efficient decoding and improved error correction without transmitter awareness of the receiver's side information.

Contribution

The paper develops novel algebraic error correcting codes, including cyclic and MDS codes, optimized for informed receivers with side information, enhancing error correction and decoding efficiency.

Findings

Codes are of short block length

Many codes achieve near-optimal error correction

Codes provide larger minimum distances than existing ones

Abstract

We construct error correcting codes for jointly transmitting a finite set of independent messages to an 'informed receiver' which has prior knowledge of the values of some subset of the messages as side information. The transmitter is oblivious to the message subset already known to the receiver and performs encoding in such a way that any possible side information can be used efficiently at the decoder. We construct and identify several families of algebraic error correcting codes for this problem using cyclic and maximum distance separable (MDS) codes. The proposed codes are of short block length, many of them provide optimum or near-optimum error correction capabilities and guarantee larger minimum distances than known codes of similar parameters for informed receivers. The constructed codes are also useful as error correcting codes for index coding when the transmitter does not know the side information available at the receivers.