Code constructions for asynchronous random multiple-access to the adder channel

A situation where up to T randomly chosen users, out of M potential ones, simultaneously transmit data over the noiseless adder channel (AC) is considered. These T (or less) active users operate independently, and because of unknown time offsets among their clock, and different delays that the various messages incur during transmission, both block and bit synchronism are precluded. Code constructions that ensure error-free asynchronous communication over the adder channel are presented. The information rate of these codes approaches 1/T bits per user. If exactly T users are active, use of these codes leads to an aggregate rate arbitrarily close to 1 bit per channel use