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

Mahesh, AA and Rajput, C and Rupa, B and Rajan, BS (2023) Average Probability of Error for Single Uniprior Index Coding over Rayleigh Fading Channel. In: 2023 IEEE Information Theory Workshop, ITW 2023, 23 - 28 April 2023, Saint-Malo, pp. 418-423.

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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.

Item Type:	Conference Paper
Publication:	2023 IEEE Information Theory Workshop, ITW 2023
Publisher:	Institute of Electrical and Electronics Engineers Inc.
Additional Information:	The copyright for this article belongs to the Institute of Electrical and Electronics Engineers Inc.
Keywords:	Decoding; Fading channels; Flow graphs; Graphic methods; Optimal systems; Rayleigh fading; Trees (mathematics), Average probability of error; Coding problems; Index coding; Information flow graphs; Min-max; Number of transmissions; Probabilities of error; Rayleigh-fading channel; Spanning tree; Strongly connected component, Errors
Department/Centre:	Division of Electrical Sciences > Electrical Communication Engineering
Date Deposited:	01 Aug 2023 05:08
Last Modified:	01 Aug 2023 05:08
URI:	https://eprints.iisc.ac.in/id/eprint/82749

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