  This paper presents generalized channel coding theorems for a time-slotted
distributed communication system where a transmitter-receiver pair is
communicating in parallel with other transmitters. Assume that the channel code
of each transmitter is chosen arbitrarily in each time slot. The coding choice
of a transmitter is denoted by a code index parameter, which is known neither
to other transmitters nor to the receiver. Fundamental performance limitation
of the system is characterized using an achievable region defined in the space
of the code index vectors. As the codeword length is taken to infinity, for all
code index vectors inside the region, the receiver will decode the message
reliably, while for all code index vectors outside the region, the receiver
will report a collision reliably. A generalized system error performance
measure is defined as the weighted sum of probabilities of different types of
communication error events. Assume that the receiver chooses an "operation
region" and intends to decode the message if the code index vector is inside
the operation region. Achievable bounds on the tradeoff between the operation
region and the generalize error performance measure are obtained under the
assumption of a finite codeword length.
