A class of capacity-achieving, low-complexity, high-reliability, variable-rate coding schemes is developed for communication over discrete memoryless channels with noiseless feedback. Algorithms for encoding and decoding that require computations growing linearly with the number of channel inputs used are developed. The error exponent associated with the scheme is shown to be optimal and implies that capacity is achievable. Simulations are performed and support the analytically predicted high performance and low complexity.

The problem of estimating parameters of discrete-time non-Gaussian autoregressive (AR) processes is addressed. The subclass of such processes considered is restricted to those whose driving noise samples are statistically independent and identically distributed according to a Gaussian-mixture probability density function (PDF). Because the likelihood function for this problem is typically unbounded in the vicinity of undesirable, degenerate parameter estimates, a global maximum likelihood approach is not appropriate. Hence, an alternative approach is taken whereby a finite local maximum of the likelihood surface is sought. This approach, which is termed the quasi-maximum likelihood (QML) approach, is used to obtain estimates of the AR parameters as well as the means, variances, and weighting coefficients that define the Gaussian-mixture PDF. A technique for generating solutions to the QML problem is derived using a generalized version of the expectation-maximization principle.

A wavelet-transform-based CELP coder design is presented in this paper for high-quality speech coding at about 4.8 kbits/s. The coder quantizes the second residual using a wavelet transform approach instead of the stochastic-codebook-based vector quantization normally used in CELP coders, including the U.S. Federal Standard FS 1016 coder at 4.8 kbits/s. The wavelet coder improves the computational efficiency for encoding the second residual by requiring only 1.2 MIPS instead of 8.3 MIPS required by FS 1016. Subjective speech quality tests involving pairwise comparisons show that the wavelet coder was preferred 61% of the time over FS 1016.>