Error Exponent for Multiple-Access Channels: Upper Bounds
The problem of bounding the reliability function of a Multiple-Access Channel (MAC) is studied. Two new upper bounds on the error exponent of a two-user Discrete Memoryless (DM) Multiple-Access Channel (MAC) are derived. The first bound (sphere packing) is an upper bound on the average error exponent and is the first bound of this type that explicitly imposes independence of the users' input distributions (conditioned on the time-sharing auxiliary variable) and thus results in a tighter sphere-packing exponent when compared to the tightest known exponent derived by Haroutunian. The second bound (minimum distance) is an upper bound on the maximal error exponent and not the average. To obtain this bound, first, an upper bound on the minimum Bhattacharyya distance between codeword pairs is derived.