In using digital speech for mobile radio, we encounter the problem of severe bit-error bursts. Error clustering occurs because the bit duration is typically much smaller than that of a signal “fade,” and average bit-error probabilities greater than 1 percent are not uncommon. For speech communication over such channels, this paper proposes variable step-size differential coders based on explicit (and error-protected) transmission of quantizer step size. Specifically, we discuss delta and dpcm coders to be referred to as dm-aqf and dpcm-aqf, where aqf stands for adaptive quantization with forward estimation (and transmission) of step size. (Backward estimation, based on quantized-signal history, has the nice feature that the step-size information does not have to be explicitly transmitted. Furthermore, obtaining this information does not entail any encoding delay. However, due to the dependence of step size on reconstructed signal history, backward estimation is often less reliable in the presence of bit errors than a scheme based on aqf.) The studies reported in this paper cover the problem of step-size determination in aqf, the design of time-invariant first-order predictors for dpcm-aqf, and the performances of aqf encoders with and without burst-error-protecting ploys such as redundant time-diversity coding and bit scrambling. Judging from snr figures and informal listening tests, interesting results are obtained with the following 48-kb/s coders: three-bit dpcm-aqf with redundant error protection, and dm-aqf using bit scrambling.