The problem is considered of encoding a discrete memoryless source when correlated side information may or may not be available to the decoder. It is assumed that the side information is not available to the encoder. The rate-distortion function R(D,, D2) is determined where D, is the distortion achieved with side information and D, is the distortion achieved without it. A generalization is made to the case of m decoders, each of which is privy to its own side information. An appropriately defined D-admissible rate for this general case is shown to equal R(D) when the side information sources satisfy a specified degradedness condition. Explicit results are obtained in the quadratic Gaussian case and in the binary Hamming case.

A computer memory with defects is modeled as a discrete memoryless channel with states that are statistically determined. The storage capacity is found when complete defect information is given to the encoder or to the decoder, and when the defect information is given completely to the decoder but only partially to the encoder. Achievable storage rates are established when partial defect information is provided at varying rates to both the encoder and the decoder. Arimoto-Blahut type algorithms are used to compute the storage capacity.

Delayed decision-feedback sequence estimation (DDFSE) is a detection algorithm that prpvides a direct tradeoff between complexity and performance in digital co~munications over intersymbol interference channels. The complexity of the algorithm is controlled by a pqrameter p and can be varied from zero tfl the lpemory of the channel (which can be infinite). The algorithq is based on a trellis with the number of states exponential in p. Whey p = Q, QDFSE requces to the decision-feedback detector. When the qemory of the channel is finite, PDFSE with maximal complexity i w equivaleat to the Viterbi slgoritbm. Of course, if the channel has infinite mepory, the Viterbi algorithm cannot be implemented. Far the intermediate values of p, the algorithm can be described as a reduced-state Viterbi algorithm with feedback incorporated into the structure of path metric computations.We first consider DDFSE for uncoded PAM signals. Estimates on the performance of the algorithm are given, and simulation results are provided for several examples. A more general form of DDFSE applicable to coded modulation systems is also presented. As an example, detection of trellis coded QPSK signals over intersymbol interference channels is discussed., m f -, , xi-into u, = ( m f -, , mj-,) and u, = x,-I . The dranch metric is ( y , -t, 1 where t, = x, + G,-,, and from (10) and (1 I), the partial state estimator is given by v^(u,, m ! , m f ) = x,(x, = x ( m ! , m2, u,) J J J is determined by (36), and w,- = -pu(u,)). Fig. 10 shows results of computer simulations for this channel ( p = 1/2). It gives error rates of the DDFSE and the

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