Anytime coding on the infinite bandwidth AWGN channel: A sequential semi-orthogonal code

It is well known that orthogonal coding can be used to approach the Shannon capacity of the power-constrained AWGN channel without a bandwidth constraint. In this paper, I show that it is possible to do this using a semi-orthogonal variation of pulse position modulation that is sequential in nature — bits can be “streamed out” without having to buffer up blocks of bits at the transmitter. Maximum-likelihood decoding of the code results in an exponentially small probability of error as a function of tolerated receiver delay and thus eventually a zero probability of error on every transmitted bit. Just as orthogonal coding is related to the idea of capacity per unit cost, this code suggests an interesting sequential version of that problem.