This paper considers the estimation of the parameters of a linear discrete-time system from noisy input and output measurements. The conditions imposed on the system are quite general. The proposed method makes use of an instrumental variable (IV) vector whose cross-covariance with the system's regression vector is pre- and post-multiplied by some prechosen weights. The singular vectors of this matrix possess complete information on the system parameters. A weighted sub-space fitting (WSF) method is then applied to these singular vectors to consistently estimate the parameters of the system. The proposed method is non-iterative, easy to implement and has a small computational burden. The asymptotic distribution of its estimation errors is derived and the result is used to motivate the choice of the weighting matrix in the WSF step and also to predict the estimation accuracy. A numerical example is included to illustrate the performance.

A fast algorithm for searching a tree (FAST) is presented for computing the distance spectrum of convolutional codes. The distance profile of a code is used to limit substantially the error patterns that have to be searched. The algorithm can easily be modified to determine the number of nonzero information bits of an incorrect path as well as the length of an error event. For testing systematic codes, a faster version of the algorithm is given. FAST is much faster than the standard bidirectional search. On a microVAX, d/sub infinity /=27 was verified for a rate R=1/2, memory M=25 code in 37 s of CPU time. Extensive tables of rate R=1/2 encoders are given. Several of the listed encoders have distance spectra superior to those of any previously known codes of the same rate and memory. A conjecture than an R=1/2 systematic convolutional code of memory 2M will perform as well as a nonsystematic convolutional code of memory M is given strong support.>

An upper bound on the first-event error probability for maximum-likelihood decoding of fixed binary convolutional codes on the binary symmetric channel is derived. The bound is evaluated for rate1/2codes, and comparisons are made with simulations and with the bounds of Viterbi, Van de Meeberg, and Post. In particular, the new bound is significantly better than Van de Meeberg's bound for rates aboveR_{\comp}.

A class of perfect block codes are found for the binary channel associated with differentially encoded phase shift keying signals with coherent detection (DCPSK). The codes are shown to correct all double adjacent errors and single errors in the first and last word positions. Such codes are found for which the number of available different syndromes equals the number of most probable channel errors. A construction algorithm is given for this class of codes. Computer search results for shortened codes are presented.