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A differential pulse code modulation (DPCM) system having adaptive quantization with forward (AQF) transmission of step-size, and second-order predictors that are adaptive and operate on the locally decoded speech signal, is proposed. For a transmission rate of 40 kbits/s, a block size of 256 speech samples, the DPCM-AQF system using the sequential gradient estimation predictor (SGEP) has segmental signal-to-noise ratio (SNR) gains of 3 and 9 dB compared to the stochastic approximation predictor (SAP) and the leaky integrator, respectively. The dynamic range of the DPCM-AQF using SGEP for an SNR of 35 dB is 30 dB, and it is insensitive to block size (<512). When transmission errors are introduced, it has a higher SNR than that achieved with the leaky integrator for bit error rates <0.08 percent.