Finite-Blocklength Approximations for Noncoherent Rayleigh Block-Fading Channels

Several emerging wireless communication services\ua0and applications have stringent latency requirements, necessitating the transmission of short packets. To obtain performance benchmarks for short-packet wireless communications, it is crucial to study the maximum coding rate as a function of the blocklength, commonly called finite-blocklength analysis. A finiteblocklength analysis can be performed via nonasymptotic bounds or via refined asymptotic approximations. This paper reviews finite-blocklength approximations for the noncoherent Rayleigh block-fading channel. These approximations have negligible computational cost compared to the nonasymptotic bounds and are shown to be accurate for error probabilities as small as 10^-8 and SNRs down to 0 dB