Random coding in noise-free multiple access networks over finite fields

Abstract

A two transmitter single receiver multiple access noise-free network is considered where interference is additive and the transmit and receive alphabet size is the same. We consider two performance metrics - code rate and sum rate. Code rate is defined as the ratio of the symbols recovered, after multiple access interference, to the symbols sent by the transmitters. The sum rate is the number of symbols successfully received per unit time. A packet by packet coding scheme is presented where we determine how these rates change with redundancy. We propose a coding mechanism that maximizes the code and sum rates and show that it suffices to code at only one of the transmitters and that systematic codes are sufficient for this purpose. The development is independent of the alphabet size the symbols are defined over. We also show that we can achieve maximum rates by using a random code. This allows us to choose codes in a random fashion and the scheme achieves optimality with probability tending to 1 exponentially with the code length.