Bounds on the Second-Order Coding Rate of the MIMO Rayleigh Block-Fading Channel
The channel capacity describes the maximal rate at which data exchange with vanishing error probability is possible, provided that the length of each codeword is allowed to grow without limit. By focusing on this asymptotic limit, the theory of information ignores the role of delay as an important parameter. Although the channel capacity and the related Shannon theory constitute a scientific success story, in many real-world applications, relatively short block lengths are required due to either delay and/or complexity constraints. The authors study the second-order coding rate of the Multiple-Input Multiple-Output (MIMO) Rayleigh block-fading channel via statistical bounds from information spectrum methods and random matrix theory.