Convolution represents a major computational load for many scientific and engineering applications, including seismic surface simulations and seismic imaging. Since convolution presents a heavy computational load, increasing its efficiency can significantly enhance the performance of associated applications. In this work, we present an in-depth analysis of the convolution algorithm and its complexity in order to develop adequate parallel algorithms. The implementation of these algorithms and their evaluation on the IBM Cell Broadband Engine (BE) processor reveals the gains and losses achieved by parallelizing the direct convolution. The performance results show that despite the complexity of the convolution processing, a speedup gain of at least 71.4 is obtained. The parallel vectorized algorithm requires the development effort of considering three independent vectorization strategies. Given the wide availability of Cell processors, the proposed parallelization approach can be widely adopted by any convolution-based application.

An important step toward achieving a high-quality 4 kb/s speech codec is reducing the coding-rate of the stochastic codebook component to near 2 kb/s. The increased reconstruction error in the residual that such low-rate quantization implies motivates the search for techniques that reduce the perceptibility of the errors in the reconstructed signal. Pitch-synchronous estimation of the linear-prediction filter and pitch-synchronous updating of the adaptive codebook reduce the coefficient-estimation error and increase the relative contribution of the adaptive codebook component to the synthesized signal, thereby reducing audible noise. However, pitch synchronous analysis normally results in a variable-rate coder. To obtain a fixed-rate representation, we introduce an efficient representation of the stochastic codebook component using a pulse density of one pulse per 2 ms and signed magnitudes specified by 2 bits per pulse-pair. The resulting reconstructions are evaluated for CELP coders corresponding to classical and generalized-pitch-predictor designs. In both cases speech quality comparable to 8 kb/s G.729 is achieved.