T1 clock recovery equipment requires that transmitted data not contain long sequences of 0 bits. For this reason, equipment that interfaces to T1 networks must meet a ones-density specification that ensures that 1 bit occurs frequently enough. Most schemes for meeting this specification require a substantial amount of overhead that consumes a significant portion of the available bandwidth. In this paper, and approach that meets the ones-density requirement with very little wasted bandwidth is described. Two practical coding schemes based on the approach are presented. The first, a block coding scheme, requires an overhead rate on the order of one bit per T1 frame, along with a delay of several frames. In an error-free channel, it introduces some errors, the rate of which is made acceptably low by using sufficient delay and overhead. In an errored channel, extension of errors is negligible. The second scheme, a sliding code scheme, requires an overhead rate on the order of a fraction of a bit per T1 frame, along with a delay of only several bit times. In an error-free channel, the rate of errors introduced is negligible. In an errored channel, approximately one out of every 2000 channel errors is extended into a burst, the length of which can be made acceptably low by using sufficient overhead.>

This paper investigates the use of a fuzzy vector quantizer (FVQ) as the front end for a hidden Markov modeling (HMM) scheme for isolated word recognition. Unlike a standard vector quantizer that generates the index of a single codeword that best matches an input vector, an FVQ generates a vector whose components represent the degree to which each codeword matches the input vector. The HMM algorithm is generalized to accommodate the FVQ output. This approach is tested on a database of isolated words from a single male speaker. It is seen that the FVQ front end significantly reduces the amount of data needed to train the HMM algorithm.

The fuzzy c-means/ISODATA algorithm is usually described in terms of clustering a finite data set. An equivalent point of view is that the algorithm clusters the support points of a finite-support probability distribution. Motivated by recent work on the hard version of the algorithm, this paper extends the definition to arbitrary distributions and considers asymptotic properties. It is shown that fixed points of the algorithm are stationary points of the fuzzy objective functional, and vice versa. When the algorithm is iteratively applied to an initial prototype set, the sequence of prototype sets produced approaches the set of fixed points. If an unknown distribution is approximated by the empirical distribution of stationary, ergodic observations, then as the number of observations grows large, fixed points of the algorithm based on the empirical distribution approach fixed points of the algorithm based on the true distribution. Furthermore, with respect to minimizing the fuzzy objective functional, the algorithm based on the empirical distribution is asymptotically at least as good as the algorithm based on the true distribution.

The generalized Lloyd algorithm for vector quantizer design is analyzed as a descent algorithm for nonlinear programming. A broad class of convex distortion functions is considered and any input distribution that has no singular-continuous part is allowed. A well-known convergence theorem is applied to show that iterative applications of the algorithm produce a sequence of quantizers that approaches the set of fixed-point quantizers. The methods of the theorem are extended to sequences of algorithms, yielding results on the behavior of the algorithm when an unknown distribution is approximated by a training sequence of observations. It is shown that as the length of the training sequence grows large that 1) fixed-point quantizers for the training sequence approach the set of fixed-point quantizers for the true distribution, and 2) limiting quantizers produced by the algorithm with the training sequence distribution perform no worse than limiting quantizers produced by the algorithm with the true distribution.