Arithmetic coding with improved solution for the carry-over problem

Abstract

Summary form only given. The carry-over problem is inherent in arithmetic coding as a result of using finite precision arithmetic. As far as we know, the currently widely used solution for this problem is the bit-stuffing technique, which was proposed by Rissanen and Langdon (198l). However, this technique is not completely satisfactory. The stuffed-bit affects the coding efficiency slightly. The code stream inserted with several stuffed-bits loses its concept as a real number. This conflicts with the principle that arithmetic coding maps an input stream to an interval on the real line, which is neither perfect nor convenient for analysis. We present our solution for the carry-over problem, the carry-trap technique, which works without the deliberately inserted stuffed-bit. We also present a concise termination method, named the medium termination technique. Both are proved rigorously.