Coding for DPSK noisy phase channels

Low to moderate complexity coding schemes are suggested and examined for binary DPSK modulation. The model of the communication channel consists of both a Brownian motion phase noise and an additive white Gaussian noise. Decoding utilizes a mismatched soft-decision metric, which comprises the prefiltering of the phase noise impaired signals followed by differential demodulation. The resulting equivalent, binary-input, output-symmetric, discrete-time, coding channel is stationary and memoryless. It accounts as well for an underlying time-diversity, thus providing an effective simple, means of boosting the capabilities of less powerful codes to cope with the existing phase noise levels. An analytical upper bound on the coded error probability is derived, which strictly addresses the Brownian motion phase model. It features a convenient decoupling of the code structure from the coding channel. The latter is completely specified via a single, scalar, generic parameter which relies on the univariate moments admitted by certain exponential functionals of the Brownian motion sample path, the exact statistics of which is intractable. The theory is illustrated while studying the performance of low constraint length, rate 1/n, binary convolutional codes, which are optimally combined with time-diversity. The advantages obtained by less trivial forms of code concatenation are examined. The approach treated is to use a two level concatenation scheme for which the binary inner code dimension matches the alphabet size of an outer non-binary code