A high degree of compression can be achieved in audio and image coding systems by using a multiple-stage lossless encoding process having low computational cost that does not require high-accuracy pre-defined probability distribution functions of the information to be compressed. The multiple-stage encoding process classifies the signal components to be compressed into one of several classifications according to signal component value. Signal components placed into higher-level classifications are represented by tokens in the lower-level classifications. Each stage of the encoding process forms groups of signal components and tokens and applies a multi-dimensional encoding process to the groups. The dimension of the coding process is equal to the size of the group to which it is applied, and is chosen to balance computational requirements of the encoding process against compression performance.