Diversity versus Channel Knowledge at Finite Block-Length

Paper in proceeding, 2012

We study the maximal achievable rate $R^{*}(n, \epsilon)$ for a given block-length $n$ and block error probability $\epsilon$ over Rayleigh block-fading channels in the noncoherent setting and in the finite block-length regime. Our results show that for a given block-length and error probability, $R^{*}(n, \epsilon)$ is not monotonic in the channel's coherence time, but there exists a rate maximizing coherence time that optimally trades between diversity and cost of estimating the channel.