 
Summary: 1
New Bounds on the Maximal Error Exponent
for MultipleAccess Channels
Ali Nazari, S. Sandeep Pradhan and Achilleas Anastasopoulos Electrical Engineering and Computer
Science Dept.
University of Michigan, Ann Arbor, MI 481092122, USA
Email: {anazari,pradhanv,anastas}@umich.edu
Abstract
The problem of bounding the reliability function of a multipleaccess channel (MAC) is studied. An upper bound
on the minimum Bhattacharyya distance between codeword pairs is derived. For a certain large class of twouser
discrete memoryless (DM) MAC, a lower bound on the maximal probability of decoding error is derived as a
consequence of the upper bound on Bhattacharyya distance. Further, an upper bound on the average probability of
decoding error is studied. It is shown that the corresponding upper and lower bounds have a similar structure. Using
a conjecture about the structure of the multiuser code, a tighter lower bound for the maximal probability of decoding
error is derived and is shown to be tight at zero rates.
I. INTRODUCTION
An interesting problem in network information theory is to determine the minimum probability of error which can
be achieved on a discrete memoryless (DM), multipleaccess channel (MAC). Ahlswede [1] and Liao [2] studied
the capacity region for MAC. Later, stronger versions of their coding theorem, giving exponential upper and lower
bounds on the error probability, were derived by numerous other authors. Slepian and Wolf [3], Dyachkov [4],
