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Ong and Ho developed optimal linear index codes for single uniprior indexcoding problems (ICPs) by finding a spanning tree for each of the stronglyconnected components of the corresponding information-flow graphs, followingwhich Thomas et al. considered the same class of ICPs over Rayleigh fadingchannel. They developed the min-max probability of error criterion for choosingan index code which minimized the probability of error at the receivers andshowed that there always exist optimal linear index codes for which anyreceiver takes at most two transmissions to decode a requested message.Motivated by the above works, this paper considers single uniprior ICPs overRayleigh fading channels for which minimizing average probability of error isshown to be a criterion for further selection of index codes. The optimal indexcode w.r.t this criterion is shown to be one that minimizes the total number oftransmissions used for decoding the message requests at all the receivers. Analgorithm that generates a spanning tree which has a lower value of this metricas compared to the optimal star graph is also presented. For a given set ofparameters of single uniprior ICPs, a lower bound for the total number oftransmissions used by any optimal index code is derived, and a class of ICPsfor which this bound is tight is identified.

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