In this paper we describe an adaptive block transform speech coding system based on vector quantization of LPC parameters. In order to account for the power fluctuations, the speech signal is normalized to have a unit-energy prediction residual The temporal variations in the short-term spectrum, on the other hand, are taken into accour by vector quantizing the UC parameters associated with the vector of speech samples and transmitting the codeword index. For each block based on the codevector associated with the input vector, an optimum bit assignment map is used to quantize the transform coefficients. We consider two types of zero memory quantizers for encoding the transform coefficients, namely the Llyod-Max quantizer and the entropy-coded quantizer. The performance of these schemes is compared with other adaptive transform coding schemes. We show by means of simulations that the system based on entropy-coded quantizer design leads to very high performance and in most cases as much as 5 dB performance improvement in terms of segmental signal-to-noise ratio is observed over the adaptive block transform coding scheme of Noll and Zelinski [1]. The effects of the bit-rate and the size of the codebook on the performance of the systems are also studied in detail.