A New Universal Random-Coding Bound for
Average Probability Error Exponent for
Ali Nazari, Achilleas Anastasopoulos and S. Sandeep Pradhan Electrical Engineering and Computer
University of Michigan, Ann Arbor, MI 48109-2122, USA
In this work, a new upper bound for average error probability of a two-user discrete memoryless (DM) multiple-
access channel (MAC) is derived. This bound can be universally obtained for all discrete memoryless MACs with
given input and output alphabets. This is the first bound of this type that explicitly uses the method of expurgation.
It is shown that the exponent of this bound is greater than or equal to those of previously known bounds.
A crucial problem in network information theory is determining the average probability of error that can be
achieved on a discrete memoryless multiple-access channel. More specifically, a two-user DM-MAC is defined by
a stochastic matrix1
W : X × Y Z, where the input alphabets, X, Y, and the output alphabet, Z, are finite sets.
The channel transition probability for sequences of length n is given by