On the proper enumeration of all finite length strings for source coding

In the proper enumeration of the binary words, the sequence is arranged as { X 1 , X 2 , X 3 , X 4 , X 5 , X 6 , X 7 , X 8 , X 9 , … } = def { 0 , 1 , 00 , 01 , 10 , 11 , 000 , 001 , 010 , … } . Simple methods for finding the index of a given word in this proper enumeration are presented and analyzed. Additionally, methods for determining the corresponding word from a given index in this enumeration are described. These methods are extended to any radix- r word system. • Efficient algorithms enable fast one-to-one source coding. • Encoding and decoding require at most n +1 digit operations in the worst case. • Binary coding uses only 6 bit operations on average, independent of source. • Radix- r enumeration is at no computational cost in the {1, …, r } number system.