New methods for multiplication-free arithmetic coding

Abstract

Summary form only given. Arithmetic coding is a well-known technique for lossless coding or data compression. We have developed two new multiplication-free methods. Our first new method is to round A to x bits instead of truncating it. Rounding is equivalent to truncating A to its x most significant bits if the (x+1)th most significant bit of A is a 0 and adding 1 to the truncated representation if the (x+1)th most significant bit is a 1. The rounding that is applied in our new method increases the complexity (compared to truncation), since, in about half of the cases, 1 has to be added to the truncated representation. As an alternative, we therefore developed a second new method, which we call "partial rounding". By partial rounding we mean that 1 is only added to the truncated representation of A in the case when the (x+1)th most significant bit is a 1 and the xth most significant bit is a 0. In the implementation this means that the xth bit of the approximation of A equals the logical OR of the xth and (x+l)th most significant bits of the original A. The partial rounding of this second new method results in the same approximation as the "full rounding" of the first method in about 75% of the cases, but its complexity is as low as that of truncation (since the complexity of the OR is negligible). Applying the various multiplication-free methods in the arithmetic coder has demonstrated that our new rounding-based method outperforms the previously published multiplication-free methods. The "partial rounding" method outperforms the previously published truncation-based methods.