Abstract: An enumerator employs “indexing volumes” as the add-on values used to compute indexes for n-item ordered sets such as symbol sequences. Each indexing volume is associated with a different class into which the allowed ordered sets are partitioned. The indexing volumes all equal or exceed the number of ordered sets that belong to their respective classes. Additionally, the indexing volumes are quantized such that each volume V equals wrs, where r is an integer greater than unity, s is a non-negative integer, w is a positive integer whose resolution is less than required for some set counts. As a result, the addition operations used to compute the indexes can be performed with limited precision, and storage requirements for the add-on values can be relatively modest. By storing less than all the volumes needed but computing the remainder from those that are stored, the storage requirement can be reduced further.

Abstract: Entropy encoders and decoders employ an entropy-pump operation. The entropy-pump operation includes classifying blocks of the input sequence's symbols in accordance with the probabilities of occurrence of those blocks' values. Entropy coding an output component that represents the sequence of classes to which the blocks belong tends to be profitable, because that component has an entropy density less than that of the input sequence. In contrast, little opportunity for compression tends to be lost by not entropy encoding an output component that represents the values of the blocks that belong to single class, because those values' probabilities of occurrence are similar.

Abstract: An enumerator employs “indexing volumes” as the add-on values used to compute indexes for n-item ordered sets such as symbol sequences. Each indexing volume is associated with a different class into which the allowed ordered sets are partitioned. The indexing volumes all equal or exceed the number of ordered sets that belong to their respective classes. Additionally, the indexing volume Vi associated with a given class of i-item equals or exceeds the sum of the indexing volumes associated with the classes that contain the (i?1)-item prefixes of the ordered sets that belong to the given class.