Optimal Index Coding with Min-Max Probability of Error over Fading Channels

TL;DR

This paper investigates optimal index coding strategies in wireless fading channels that minimize the worst-case probability of error across all receivers, providing criteria and algorithms for selecting such codes.

Contribution

It introduces a criterion for optimal index codes that minimize maximum error probability and offers an algorithm for a specific class of problems.

Findings

Careful selection of index codes significantly reduces error probability in fading channels.

The proposed algorithm effectively identifies optimal codes for minimizing maximum error.

Simulation results demonstrate the performance gains of the proposed approach.

Abstract

An index coding scheme in which the source (transmitter) transmits binary symbols over a wireless fading channel is considered. Index codes with the transmitter using minimum number of transmissions are known as optimal index codes. Different optimal index codes give different performances in terms of probability of error in a fading environment and this also varies from receiver to receiver. In this paper we deal with optimal index codes which minimizes the maximum probability of error among all the receivers. We identify a criterion for optimal index codes that minimizes the maximum probability of error among all the receivers. For a special class of index coding problems, we give an algorithm to identify optimal index codes which minimize the maximum error probability. We illustrate our techniques and claims with simulation results leading to conclude that a careful choice among the optimal index codes will give a considerable gain in fading channels.