Boosting output distributions in finite blocklength channel coding converse bounds

Point-to-point channel coding is studied in the finite blocklength regime. Many existing converse bounds involve an optimization over a distribution on the channel output. This paper provides a method for generating good, if not optimal, output distributions. In particular, given any candidate output distribution, a “boosting” procedure is given that constructs a new distribution which improves the converse bound derived from the divergence spectrum. For discrete memoryless channels, it is shown that using the i.i.d. capacity-achieving output distribution as an initial guess in this procedure results in an output distribution that is good enough to derive the third-order coding rate for most channels. The finite blocklengths bounds are then applied to the Z channel.