Combinatorial Coding and Lexicographic Ordering

Combinatorial Coding and Lexicographic Ordering

The Matlab routines in this package generate a combinatorial index of a selection of items and decode the code to produce the corresponding selection of items. Marching through the combinatorial indices produces lexicographically ordered selections. Three cases are supported: selections with no repeated items, selections with repetitions, and selections with prescribed repetition multiplicities.
The first and third cases are described in:
[1] J. P. M. Schalkwijk, “An Algorithm for Source Coding”, IEEE Trans. Inform. Theory, Vol. IT-18, no. 2, pp. 393-399, May 1972.
The second case and the theory behind all three case are described in:
[2] P. Kabal, “Combinatorial Coding and Lexicographic Ordering”, Technical Report, Dept. Electrical & Computer Engineering, McGill University, Feb. 2018 (available on-line at www-MMSP.ECE.McGill.CA).