2 research outputs found
A New Upper Bound on the Average Error Exponent for Multiple-Access Channels
A new lower bound for the average probability or error for a two-user
discrete memoryless (DM) multiple-access channel (MAC) is derived. This bound
has a structure very similar to the well-known sphere packing packing bound
derived by Haroutunian. However, since explicitly imposes independence of the
users' input distributions (conditioned on the time-sharing auxiliary variable)
results in a tighter sphere-packing exponent in comparison to Haroutunian's.
Also, the relationship between average and maximal error probabilities is
studied. Finally, by using a known sphere packing bound on the maximal
probability of error, a lower bound on the average error probability is
derived
Error Exponent for Multiple-Access Channels:Lower Bounds
A unified framework to obtain all known lower bounds (random coding, typical
random coding and expurgated bound) on the reliability function of a
point-to-point discrete memoryless channel (DMC) is presented. By using a
similar idea for a two-user discrete memoryless (DM) multiple-access channel
(MAC), three lower bounds on the reliability function are derived. The first
one (random coding) is identical to the best known lower bound on the
reliability function of DM-MAC. It is shown that the random coding bound is the
performance of the average code in the constant composition code ensemble. The
second bound (Typical random coding) is the typical performance of the constant
composition code ensemble. To derive the third bound (expurgated), we eliminate
some of the codewords from the codebook with larger rate. This is the first
bound of this type that explicitly uses the method of expurgation for 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. All these bounds can be universally
obtained for all discrete memoryless MACs with given input and output
alphabets.Comment: 46 pages, 2 figure