nd-convolutional codes: performance and structural analysis

A noncoherent coded system which incorporates convolutional codes in conjunction with multiple symbol noncoherent detection, is presented in this paper. The underlying convolutional codes are referred to as nd-convolutional codes. These codes provide a general framework for various noncoherent coding systems, including differential systems, for different models of the carrier phase. The regular structure of nd-codes facilitates the evaluation of a simple upper bound on the pairwise and bit error probability. The exponential rate of the error probability, which is the single parameter governing the error performance at large signal to noise ratios, is identified via Large Deviations techniques. This parameter leads to the interesting conclusion that increasing the branch observation interval L does not necessarily monotonically improve the error performance of the noncoherent system. The same conclusion is reached by examining the upper bounds and computer simulation results of several examples. These examples also reveal that optimal codes for coherent detection are not necessarily optimal for noncoherent detection and a search for good codes, some of which are tabulated here is required.