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. Index Terms AWGN, delay, orthogonal coding, anytime reliability, sphere-packing bounds, capacity per unit cost A. Sahai is with Wireless Foundations in the Department of Electrical Engineering and Computer Sciences, U.C. Berkeley. An early version of this paper was presented at the 2005 CISS Conference in Baltimore, MD. IEEE TRANSACTIONS ON INFORMATION THEORY, VOL. ??, NO. ??, MONTH?? 2005 1 Anytime coding on the infinite bandwidth AWGN channel: A sequential semi-orthogonal optimal code