A noncoherent coded system, which incorporates convolutional codes in conjunction of multiple symbol noncoherent detection, is presented in this two-part paper, where Part I focuses on the performance analysis of the system and Part II deals with the structural properties of the underlying convolutional codes. These convolutional codes are referred to as nd-convolutional codes. It is shown that nd-convolutional codes provide a general framework for various noncoherent coding systems, including differential systems. Two models of the carrier phase are examined and the relationships between them is established. For the first one, the carrier phase remains constant for L channels signals, whereas for the second one, it unvaries throughout the transmission period. The regular structure of nd-codes facilitates the evaluation of a simple upper bound on the pairwise and bit error probabilities, as well as a simple expression for the generalized cutoff rate. 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 L does not necessarily monotonically improve the error performance of the noncoherent system. The same conclusion is reached by examining upper bounds and computer simulation results of several interesting 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 in Part II of the paper, is required.

For pt.I see ibid., vol.43, no.2, p.558-75 (1997). The structural properties of a noncoherent coded system, which incorporates convolutional codes in conjunction with multiple symbol noncoherent detection, is presented in this second part of a two-part paper, where the performance analysis was provided in Part I. These convolutional codes are referred to as nd-convolutional codes and they provide a general framework for various noncoherent coding systems, including differential 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 equivalent distance of nd-codes, which is the single parameter dominating the error performance at large signal-to-noise ratios. The free equivalent distance is upper-bounded by the free nd-distance, which constitutes a more convenient and practical parameter to work with, and it is the basis for a computer search for optimal nd-codes. The resultant codes of the computer search are compared to codes which are optimal for coherent detection, and it is verified that the latter codes are not necessarily 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 conditions for catastrophic error propagation are identified.

This article focuses on code design and code selection rules under power and decoding delay constraints for an antipodal (BPSK) modulated and convolutionally encoded communication system. The system operates over a slowly fading AWGN channel, described by the block-fading model. We emphasize perfect coherent detection with maximum likelihood decoding assuming ideal channel information (the instantaneous fading values). The dominant design criterion in this scenario is the code diversity level in terms of blocks while the standard Hamming distance plays a secondary role. A code design procedure, based on maximum distance separable (MDS) cyclic block codes is presented along with a code-search algorithm. The performance results of selected codes are assessed via simulation and compared to those achieved by Reed-Solomon codes with erasure and error decoding.

A modified version of the multilevel coded modulation scheme of Imai and Hirakawa (1977) is presented and analyzed. In the transmitter, the outputs of the component codes are bit interleaved prior to mapping into 8-PSK channel signals. A multistage receiver is considered, in which the output amplitudes of the Gaussian channel are soft limited before entering the second and third stage decoders. Upper bounds and Gaussian approximations for the bit error probability of every component code, which take into account errors in previously decoded stages, are presented. Aided by a comprehensive computer simulation, it is demonstrated in a specific example that the addition of the interleaver and soft limiter in the third stage improves its performance by 1.1 dB at a bit error probability of 10/sup /spl minus/5/, and that the multilevel scheme improves on an Ungerboeck's code with the same decoding complexity. The rate selection of the component codes is also considered and a simple selection rule, based on information theoretic arguments, is provided.>

Bounds on the capacity of binary symmetric channels and additive Gaussian channels with run-length-limited two-level (binary, bipolar) inputs are presented, and their tightness is demonstrated for some cases. Stationary input sequences, which do not degrade capacity, are considered when deriving the bounds. Lower bounds on the magnetic recording density for a simple continuous-time recording model incorporating a minimal intertransition constraint are evaluated for soft and hard decisions. A superiority of about 1.5 dB in signal-to-noise ratio is observed for the soft-decision scheme.>