Compression of sparse matrices by arithmetic coding

Abstract

The compression of matrices where the majority of the entries are a fixed constant (most typically zero), usually referred to as sparse matrices, has received much attention. We evaluate the performance of existing methods, and consider how arithmetic coding can be applied to the problem to achieve better compression. The result is a method that gives better compression than existing methods, and still allows constant-time access to individual elements if required. Although for concreteness we express our method in terms of two-dimensional matrices where the majority of the values are zero, it is equally applicable to matrices of any number of dimensions and where the fixed known constant is any value. We assume that the number of dimensions and their ranges are known, but will not assume that any information is available externally regarding the number of non-zero entries.