  In recent years, the derivation of nonasymptotic converse and achievability
bounds on the maximum coding rate as a function of the error probability and
blocklength has gained attention in the information theory literature. While
these bounds are accurate for many scenarios of interest, they need to be
evaluated numerically for most wireless channels of practical interest, and
their evaluation is computationally demanding. This paper presents saddlepoint
approximations of state-of-the-art converse and achievability bounds for
noncoherent, single-antenna, Rayleigh block-fading channels. These
approximations can be calculated efficiently and are shown to be accurate for
SNR values as small as 0 dB and blocklengths of 168 channel uses or more.
