Adaptive Predictive Coding: Transmit signal AND prediction coefficients
This sounds like a variant of Differential Pulse-Code Modulation. In this set of techniques, the correlation of adjacent values and the effect of quantisation are exploited for "compression" (whether this is for transmission or storage). That is, instead of encoding the sample values, you encode the difference between them which, within limits, could be described by a much smaller number than the values themselves.

However, another technique that might be useful to you here is run length encoding. In run length encoding, the encoded word describes either the sample value itself or how many repetitions of the same value are to be decoded.

In either case, you would require higher bandwidth around the signal transients (many messages sent between the encoder and the decoder) and much lower during the longer times of constant values.

Hope this helps.