On the Finite Blocklength Performance of Lossy Multi-Connectivity

In this paper, we are interested in the lossy transmission of a single source over parallel additive white Gaussian noise channels with independent quasi-static fading and receiver channel state information. We call this the lossy multi-connectivity problem. Motivated by the ultra-reliable and low latency communication requirements, we consider the finite blocklength performance of lossy multi-connectivity. By generalizing the non-asymptotic bounds of Kostina and Verdti for the lossy joint source-channel coding problem, we derive nonasymptotic achievability and converse bounds for the lossy multi-connectivity problem. Using these non-asymptotic bounds, under mild conditions on the fading distribution, we derive good approximations for the finite blocklength performance in the spirit of second-order asymptotics for any discrete memoryless source under any bounded distortion measure. Our results demonstrate that the asymptotic notions of outage probability and outage capacity are actually good criteria even in the finite blocklength regime. Finally, we illustrate our results via numerical examples.

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