Multiplication-free multi-alphabet arithmetic code

Abstract

Method and apparatus which cyclically generate a compressed, arithmetically-coded binary stream in response to binary occurrence counts of symbols in an uncoded string. The symbols in the uncoded string are drawn from a multi-character alphabet which is not necessarily a binary one. Coding operations and hardware are simplified by deriving from the binary occurrence counts an estimate of the probability of each unencoded symbol at its precise lexical location. The probability estimation eliminates any requirement for division or multiplication by employing magnitude-shifting of the binary occurrence counts. The encoded stream is augmented by the estimated symbol probability at the same time that an internal variable is updated with an estimate of the portion of a probability interval remaining after coding the current symbol, the interval estimate being obtained from the left-shifted occurrence counts. Decoding is the dual of encoding. The unencoded symbol stream is extracted, symbol-by-symbol, by subtracting the estimated symbol probability that comes closest to, but does not exceed the magnitude of the compressed stream, re-estimating the symbol probabilities based upon the decoding, and testing the difference of the subtraction against the re-estimated probability.