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Rate-distortion theory provides the motivation for using data compression techniques on matrices of N LPC vectors. This leads to a simple extension of speech coding techniques using vector quantization. The effects of using the generalized Lloyd algorithm on such matrices using a summed Itakura-Saito distortion measure are studied, and an extension of the centroid computation used in vector quantization is presented. The matrix quantizers so obtained offer substantial reductions in bit rates relative to full-search vector quantizers. Bit rates as low as 150 bits/s for the LPC matrix information (inclusive of gain, but without pitch and voicing) have been achieved for a single speaker, having average test sequence and codebook distortions comparable to those in the equivalent full-search vector quantizer operating at 350 bits/s. Preliminary results indicate that higher quality or lower bit rates may be achieved with enough computational resources.