A fake process approach to data compression

The problem of designing a good decoder for a time-invariant tree-coding data compression system is equivalent to that of finding a good low rate 'fake process' for the original source, where the fake is produced by a time-invariant nonlinear filtering of an independent, identically distributed sequence of uniformly distributed discrete random variables and 'goodness' is measured by the generalized Ornstein distance between the fake and the original source. Several simple ad hoc techniques for obtaining such fake processes are introduced and shown by simulation to provide an improvement of typically 1-2 dB over optimum quantization, delta modulation, and predictive quantization for one-bit per symbol compression of Gaussian memoryless, autoregressive, and moving average sources. In addition, the fake process viewpoint provides a new intuitive explanation of why delta modulation and predictive quantization work as well as they do on Gaussian autoregressive sources.