Simple channel coding bounds

New channel coding converse and achievability bounds are derived for a single use of an arbitrary channel. Both bounds are expressed using a quantity called the ldquosmooth 0-divergencerdquo, which is a generalization of Renyi´s divergence of order 0. The bounds are also studied in the limit of large block-lengths. In particular, they combine to give a general capacity formula which is equivalent to the one derived by Verdu and Han.