For pt. I see ibid., vol.46, p.610-20 (1998). We continue the study of cut set trellis section T/sub CB/ codes begun in Part I and show that such codes are well suited for use with multiple symbol noncoherent detection and conventional two symbol differential detection. The information bit assignment for a cut set trellis section can be modified to make the resulting code noncatastrophic for noncoherent detection. By this procedure, many existing two-dimensional (2-D) and multidimensional MPSK and QAM trellis codes designed for coherent detection can be easily converted into codes for both coherent and noncoherent detection. Compared to M-DPSK trellis codes, it is shown that 2-D MPSK cut set trellis section codes have improved performance for multiple symbol noncoherent detection and comparable performance for conventional two symbol differential detection. Thus, cut set trellis section codes are a class of 'universal' channel codes since a single encoder performs well for coherent detection, multiple symbol noncoherent detection, and conventional two symbol differential detection.

Let a trellis section /spl Tscr/ generate a trellis code /spl Cscr/. We study two trellis sections based on /spl Tscr/, a "cut-set" trellis section /spl Tscr//sub cs/ and a "differential encoder" trellis section /spl Tscr//sub de/. We show that /spl Tscr/ can be transformed to a cut-set trellis section /spl Tscr//sub cs/, which is equivalent to /spl Tscr/ in the sense that both /spl Tscr/ and /spl Tscr//sub cs/ generate /spl Cscr/ and both /spl Tscr/ and /spl Tscr//sub cs/ have the same decoding complexity. A differential encoder trellis section is equivalent to the trellis section obtained by following /spl Tscr/ with a differential encoder. It is shown that both /spl Tscr//sub cs/ and /spl Tscr//sub de/ have inverse transform trellis sections. A differential encoder trellis section generates a rotationally invariant (RI) code in a particularly simple and straightforward way. But an RI code need not have a differential encoder trellis section. However, for all of the RI codes examined here, we show that the cut-set trellis section can be arranged into a differential encoder trellis section. This means that these codes can be decomposed into an encoder followed by a differential encoder. Further we show that when /spl Tscr/ is formed using a linear binary convolutional encoder and a mapping by set partitioning, then /spl Tscr/ followed by a differential encoder gives an RI code which in some cases is as good as the best previously known codes, after applying the inverse transform to /spl Tscr//sub de/.

For a small number of symbols N and slow flat fading channels, it is shown that covariance matrices encountered in practice have two nonnegligible eigenvalues, the first much larger than the second, with a symmetric eigenvector associated with the first eigenvalue, and a skew symmetric eigenvector associated with the second eigenvalue. The first eigenvector is well approximated by a conditional mean, and the second eigenvector represents a small drift about the mean. The eigenvalues and eigenvectors of the slow flat fading channel covariance matrix are shown to be strongly related to those of a certain conditional covariance matrix. The maximum likelihood (ML) rules for block hard decision and symbol-by-symbol hard decision, and a rule for soft decision detection of M-DPSK, all using multiple symbol information, are obtained for the Rician channel as a function of N. The eigenvalue-eigenvector results lead to practical implementations of all rules. For small to moderate N, it is shown that a simple open-loop algorithm, of complexity N log N, attains the performance of the ML decision rules for an E/sub s//N/sub 0/ range of interest for several land mobile satellite systems. The ML decision rules are seen to give rapidly diminishing returns as N increases, showing that simple noncoherent techniques can have very effective performance for the Rician fading channel. Lastly, several conclusions are drawn about the asymptotic channel behavior, including the Rayleigh channel. The work is directly applicable to the Australian and North American land mobile satellite systems.>

Multiple-symbol differential detection (MSDD) of differentially encoded MPSK uses maximum likelihood sequence detection of N symbols to achieve a performance gain over conventional 2 symbol differential detection. The paper gives a fast (optimum) algorithm to implement MSDD. The number of operations per N symbol block is of order Nlog/sub 2/ N.>

Maximum likelihood sequence detection (MLSD) of differentially encoded MPSK uses a joint decision on N symbols to achieve a performance gain over conventional 2 symbol differential detection. This paper gives a fast (optimum) algorithm to implement MLSD; the number of operations per N symbol block is of order N log/sub 2/ N. Thus, it is practical to implement MLSD for any reasonable N for moderate symbol rates; this is useful for the land mobile satellite and digital cellular channels.>

Recently Gallager has given the construction for an optimal source code for geometrically distributed integer alphabets. Gallager's code can be modified to perform as a universal code for the memoryless binary source; this code construction has several important practical advantages over previous universal codes for the binary source.

Correlated information sequences\{X_{i}\}and\{Y_{i}\}are generated by a source and receiver, respectively. The least number of bits per source character that must be given to the receiver to allow perfect detection of errors in the sequence\{Y_{i}\}is found. The performance of error detecting codes used over noisy channels is characterized by this result.

Wyner and Ziv considered the problem of source encoding and decoding when the decoder knows a random variableYcorrelated with the sourceX. The least rateRfor which the system can operate with fidelitydia given ia terms of an information theoretic minimizationR\ast (d). Explicit upper and lower bounds toR\ast (d)are given for an important class of correlated sources. The upper and lower bounds have been evaluated for several members of the class and are shown to agree in these cases.

Variable-rate universal source codes are data compression schemes that are optimum for the coding of a collection of sources (e.g., a source with unknown parameters) subject to a fixed average distortion constraint. Existence of variable-rate universal source codes is demonstrated for very general classes of sources and distortion measures.

Discrete-time source coding theorems are established for more general reproduction alphabets than allowed in previous results on coding for a class of sources subject to a fidelity constraint. The two different alphabets considered are metric spaces for which every closed bounded subset is compact and separable Hilbert spaces. Potential applications of the Hilbert space results to continuous-time source coding are discussed.