Ong and Ho developed optimal linear index codes for single uniprior index coding problems (ICPs) by finding a spanning tree for each strongly connected component of their information-flow graphs, following which Thomas et al. considered the same class of ICPs over Rayleigh fading channels. They developed the min-max probability of error criterion for choosing an index code from the set of bandwidth-optimal linear index codes. Motivated by the above works, this paper deals with single uniprior ICPs over binary-input continuous-output channels. Minimizing the average probability of error is introduced as a criterion for further selection of index codes which is shown to be equivalent to minimizing the total number of transmissions used for decoding the message requests at all the receivers. An algorithm that generates a spanning tree with a lower value of this metric than the optimal star graph is also presented. A couple of lower bounds for the total number of transmissions, used by any optimal index code, are derived, and two classes of ICPs for which these bounds are tight are identified. An improvement of the proposed algorithm for information-flow graphs with bridges and a generalization of the improved algorithm for information-flow graphs obtainable as the union of strongly connected sub-graphs are presented, and some optimality results are derived.

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.