Sequential random coding error exponents for multiple access channels

Discrete-time memoryless multiple access channels (MACs) are a useful abstraction of the uplink for many centralized wireless systems. They capture the issues involved with many different users wanting to simultaneously send information to a single site. Traditional MAC analysis proceeds in the context of block codes with the messages being known in advance by the encoders. Instead, we look at a sequential setting. Each user's message evolves in real-time as bits stream in to the encoders. In this context, we look at the probability of error not at the block level, but at the bit-level. Furthermore, in place of block-length, we look at the delay between when the bit arrives at the encoder and when it is decoded by the central decoder. The sequential random coding error exponent is studied and shown to be positive in the whole achievable rate region for multiple access channels. Furthermore, we show that this exponent can be achieved in a delay-universal or "anytime" fashion in that the encoder does not have to specify the target delay. The choice of decoding delay is left up to the decoder which is free to vary this on an application specific basis - the longer it is willing to wait, the lower the probability of bit error will be.