A sub-band speech coding arrangement divides the speech spectrum into sub-bands and allocates bits to encode the time frame interval samples of each sub-band responsive to the speech energies of the sub-bands. The sub-band samples are quantized according to the sub-band energy bit allocation and the time frame quantized samples and speech energy signals are coded. A signal representative of the residual difference between the each time frame interval speech sample of the sub-band and the corresponding quantized speech sample of the sub-band is generated. The quality of the sub-band coded signal is improved by selecting the sub-bands with the largest residual differences, producing a vector signal from the sequence of residual difference signals of each selected sub-band, and matching the sub-band vector signal to one of a set of stored Gaussian codebook entries to generate a reduced bit code for the selected vector signal. The coded time frame interval quantized signals, speech energy signals and reduced bit codes for the selected residual differences are combined to form a multiplexed stream for the speech pattern of the time frame interval.