Anytime coding on the infinite bandwidth AWGN channel: A sequential semi-orthogonal optimal 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. This correspondence describes a semi-orthogonal variation of pulse position modulation that is sequential in nature -- bits can be ``streamed across'' without having to buffer up blocks of bits at the transmitter. ML decoding 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. In the high-rate regime, a matching upper bound is given on the delay error exponent. We close with some comments on the case with feedback and the connections to the capacity per unit cost problem.