Asymptotically robust communication using an orthogonal codebook over energy-limited channels

The authors consider a stationary discrete-time memoryless communication channel with a binary input alphabet and real-valued output. An orthogonal codebook with M words is constructed, for which the nonzero components of distinct codewords do not overlap. The block length of this code is M×N, where N is the number of degrees of freedom used per codeword. A class of asymptotically robust detectors is constructed among which is the quadratic functional. The reception of general stochastic signals in additive white Gaussian noise is considered. The optimum kernel of the quadratic functional is shown to be the resolvent kernel for the covariance function of the stochastic signal. The authors specialize to the coherent lightwave channel which presents both AWGN and Brownian phase noise. It is concluded that the (suboptimal) correlation kernel features the same functional dependency on the SNR (defined at the Brownian-phase linewidth) as does the optimal detector. For large SNR and long correlation time, the optimum kernel reduces to a time-invariant singly-resonant realizable filer, and thus facilitates a simple implementation