1. In a data transmission system, a data compression system comprising: means for inputting a first set of data representing an alphabet of source symbols including a current symbol; means for generating for each source symbol an arithmetic representation of a successive subinterval within a predetermined interval, the width of each subinterval being equal to the width of the previous subinterval weighted by the current symbol's frequency of occurrence; means for approximating the width of a new subinterval with a single shift and add operation as a function of both the width of the current subinterval and a total count of source symbols in a statistical source model; and means for outputting a second set of data based on the arithmetic representations, whereby the second set of data is a compressed representation of the alphabet of source symbols.