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Hypergraph-based Source Codes for Function Computation Under Maximal Distortion

Sourya BasuDaewon SeoLav R. Varshney
Apr 2022
摘要
This work investigates functional source coding problems with maximaldistortion, motivated by approximate function computation in many modernapplications. The maximal distortion treats imprecise reconstruction of afunction value as good as perfect computation if it deviates less than atolerance level, while treating reconstruction that differs by more than thatlevel as a failure. Using a geometric understanding of the maximal distortion,we propose a hypergraph-based source coding scheme for function computationthat is constructive in the sense that it gives an explicit procedure fordefining auxiliary random variables. Moreover, we find that thehypergraph-based coding scheme achieves the optimal rate-distortion function inthe setting of coding for computing with side information and the Berger-Tungsum-rate inner bound in the setting of distributed source coding for computing.It also achieves the El Gamal-Cover inner bound for multiple description codingfor computing and is optimal for successive refinement and cascade multipledescription problems for computing. Lastly, the benefit of complexity reductionof finding a forward test channel is shown for a class of Markov sources.
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