  This paper introduces equal-image-size source partitioning, a new tool for
analyzing channel and joint source-channel coding in a multi-terminal discrete
memoryless channel environment. Equal-image-size source partitioning divides
the source (combination of messages and codewords) into a sub-exponential
number of subsets. Over each of these subsets, the exponential orders of the
minimum image sizes of most messages are roughly equal to the same entropy
term. This property gives us the strength of minimum image sizes and the
flexibility of entropy terms. Using the method of equal-image-size source
partitioning, we prove separate necessary conditions for the existence of
average-error and maximum-error codes. These necessary conditions are much
stronger than the standard Fano's inequality, and can be weakened to render
versions of Fano's inequality that apply to codes with non-vanishing error
probabilities. To demonstrate the power of this new tool, we employ the
stronger average-error version of Fano's inequality to prove the strong
converse for the discrete memoryless wiretap channel with decaying leakage,
which heretofore has been an open problem.
