Compression of sparse matrices by blocked Rice coding

This correspondence considers the compression of matrices where the majority of the entries are a fixed constant (most typically zero), usually referred to as sparse matrices. We show that using Golomb or Rice encoding requires significantly less space than previous approaches. Furthermore, compared to arithmetic coding, the space requirements are only slightly increased but access is ten times faster for both Golomb and Rice encoding. By blocking the data, the access time can be kept constant as only a single block needs to be decoded to access any element. Although such blocking increases the space overheads, this is marginal until the block sizes become so small that only a few nonzero values will be found in a block. We provide formulas giving the space overhead of blocked Rice encoding and validate these empirically.