Average Probability of Error for Single Uniprior Index Coding over Rayleigh Fading Channel

TL;DR

This paper investigates the average probability of error in single uniprior index coding over Rayleigh fading channels, proposing an optimal coding criterion that minimizes total transmissions and presenting algorithms and bounds for such codes.

Contribution

It introduces a new criterion based on average probability of error for selecting index codes and provides algorithms and bounds for optimizing transmission efficiency.

Findings

Optimal index code minimizes total number of transmissions.

A spanning tree algorithm improves upon star graph structures.

A lower bound for total transmissions is derived and tight for certain ICPs.

Abstract

Ong and Ho developed optimal linear index codes for single uniprior index coding problems (ICPs) by finding a spanning tree for each of the strongly connected components of the corresponding information-flow graphs, following which Thomas et al. considered the same class of ICPs over Rayleigh fading channel. They developed the min-max probability of error criterion for choosing an index code which minimized the probability of error at the receivers and showed that there always exist optimal linear index codes for which any receiver takes at most two transmissions to decode a requested message. Motivated by the above works, this paper considers single uniprior ICPs over Rayleigh fading channels for which minimizing average probability of error is shown to be a criterion for further selection of index codes. The optimal index code w.r.t this criterion is shown to be one that minimizes the total number of transmissions used for decoding the message requests at all the receivers. An algorithm that generates a spanning tree which has a lower value of this metric as compared to the optimal star graph is also presented. For a given set of parameters of single uniprior ICPs, a lower bound for the total number of transmissions used by any optimal index code is derived, and a class of ICPs for which this bound is tight is identified.