Arithmetic coding in lossless waveform compression

A method for applying arithmetic coding to lossless waveform compression is discussed. Arithmetic coding has been used widely in lossless text compression and is known to produce compression ratios that are nearly optimal when the symbol table consists of an ordinary alphabet. In lossless compression of digitized waveform data, however, if each possible sample value is viewed as a “symbol” the symbol table would be typically very large and impractical. the authors therefore define a symbol to be a certain range of possible waveform values, rather than a single value, and develop a coding scheme on this basis. The coding scheme consists of two compression stages. The first stage is lossless linear prediction, which removes coherent components from a digitized waveform and produces a residue sequence that is assumed to have a white spectrum and a Gaussian amplitude distribution. The prediction is lossless in the sense that the original digitized waveform can be recovered by processing the residue sequence. The second stage, which is the subject of the present paper, is arithmetic coding used as just described. A formula for selecting ranges of waveform values is provided. Experiments with seismic and speech waveforms that produce near-optimal results are included