ND-CONVOLUTIONAL CODES .2. STRUCTURAL-ANALYSIS

The structural properties of a noncoherent coded system, which incorpo rates convolutional codes in conjunction with multiple symbol noncoher ent detection, is presented in this second part of a two-part paper, w here the performance analysis was provided in Part I, These convolutio nal codes are referred to as nd-convolutional codes and they provide a general framework for various noncoherent coding systems, including d ifferential systems, for several practical models of the carrier phase , The exponential rate in which the error probability decays to zero, derived in Part I of the paper, is used here to obtain the free equiva lent distance of nd-codes, which is the single parameter dominating th e error performance at large signal to-noise ratios, The free equivale nt distance is upper-bounded by the free nd-distance, which constitute s a more convenient and practical parameter to work with, and it is th e basis for a computer search for optimal nd-codes. The resultant code s of the computer search are compared to codes which are optimal for c oherent detection, and it is verified that the latter codes are not ne cessarily optimal for noncoherent detection since they exhibit in many cases a relatively small nd-distance. The ambiguity problem, inherent to noncoherent systems, is also treated in this paper in the general framework of nd-catastrophic codes, and necessary and sufficient condi tions for catastrophic error propagation are identified.