Generalized cut‐off rate of DPSK noisy‐phase channels

Coded communication is examined for binary differential phase shift keying (DPSK) modulation where the communication channel consists of both a Brownian Motion phase noise and an additive white Gaussian noise (AWGN). Decoding utilizes a mismatched soft‐decision metric that accounts for the prefiltering of the phase‐noise‐impaired signals followed by differential demodulation. Binary Multiplexing of the equivalent channel results in a binary‐input, output‐symmetric, discrete‐time, coding channel, which is both stationary and memoryless. This multiplexing accounts as well for an underlying time‐diversity (repetition codes), providing an effective, yet simple, means of boosting the capabilities of less powerful codes to cope with high phase‐noise levels. The cut‐off rate of the considered channel is analytically too complicated to compute. The approach taken yields a coding channel characterization that further generalizes the concept of the generalized cut‐off rate for mismatched metrics to account as well for incomplete statistical characterization. The theoretical implication of this criterion for coded communication is examined. The Brownian Motion phase model is characterized by a finite set of the univariate moments admitted by certain exponential functional of the phase sample path, whose exact statistics seem intractable.