Error Exponent for Multiple-Access Channels: Lower Bounds

A unified approach is presented for the derivation of reliability function lower bounds for the two-user discrete memoryless (DM) multiple-access channel (MAC). In particular, three lower bounds are presented. The first one (random coding) is identical to the best known lower bound on the reliability function of DM-MACs. It is shown that the random coding bound characterizes the performance of the average code in the constant-type code ensemble. The second bound (typical random coding) characterizes the typical performance (the performance of a high probability subset of the ensemble) of the constant-type code ensemble. To derive the third bound (expurgated), we eliminate some of the codewords from each of the codebooks. This is the first bound of this type that explicitly uses the method of expurgation for DM-MACs. It is shown that the exponent of the typical random coding and the expurgated bounds are greater than or equal to the exponent of the known random coding bounds for all rate pairs. Moreover, an example is given where the exponent of the expurgated bound is strictly larger for a certain input distribution. Each of the presented bounds is universal in the sense that there exists a code that attains the bound for all channels with given input and output alphabets. The approach presented for the DM-MAC is first demonstrated for the point-to-point discrete memoryless channel (DMC), by rederiving the random coding and expurgated exponents, and deriving a bound that characterizes the typical performance of the constant-type code ensemble.