CODING FOR DPSK NOISY PHASE CHANNELS

Low to moderate complexity coding schemes are suggested and examined for binary differential phase shift keying (DPSK) modulation. The model of 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, which comprises the prefiltering of the phase noise impaired signals followed by differential (delay and multiply) demodulation. The resulting equivalent, binary-input, output-symmetric, discrete-time, coding channel is both stationary and memoryless. It accounts as well for an underlying time-diversity (repetition codes), thus providing an effective, yet 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 later 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 also 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. Specifically, the outer codes illustrated are the Dual-K convolutional codes and the Reed-Solomon block codes, whereas the inner codes are either simplex (Maximal Length) or bi-orthogonal (first order Reed-Muller and Hadamard codes). The numerous codes constructed facilitate high-speed data applications and are appropriately selected to meet the channel phase noise level. Compared with uncoded diversity schemes, the respective coding gains as well as the ease of bandwidth requirements are significant with just feasible low complexity schemes. The comprehensive data provided here applies to a variety of operating conditions and indicates that coding is an effective, yet simple, counter measure against phase noise. The unified approach for upper bounding the coded error probability is rigorous, yet it features a computational simplicity that makes the analysis especially suitable for a comprehensive study of the benefits of coding with soft-decision metrics.