Abstract: A method and apparatus for data, image, video, acoustic, multimedia and general multilevel digital source compression in both lossless and lossy modes is described. The method is universal (no knowledge of source statistics required) and asymptotically optimal in terms of Shannon's noiseless coding theorem. The method utilizes a random walk in Pascal's hypervolume (a multi-dimensional generalization of Pascal's triangle) starting at the apex and proceeding downward, which is directed by the incoming source sequence according to an algorithm, until it terminates at a boundary which has been constructed in such a way that the encoding of each variable length source sequence can be accomplished in a fixed number of bits. Codewords and decoded source sequences can either be computed at the encoder and decoder, respectively, or precomputed and stored at those respective locations. A preprocessing module is used to set up the data for lossless data or image compression.