11. The system of claim 10 , wherein the one or more field programmable gate arrays are further configured to compute k=C(a)+O(a, k−1)+1 and compute l=C(a)+O(a, l); wherein C(a) is a count array having a number of characters in the reference data string which are lexicographically smaller than “a” and wherein O(a,i) is an occurrence array having a count of a number of occurrences of “a” in the first “i” characters of a Burrows-Wheeler Transform string of the FM-index.
10. The system of claim 1 , wherein the one or more field programmable gate arrays are further configured to determine whether a difference between an upper bound “l” of the first or next suffix array interval and a lower bound “k” of the first or next suffix array interval is greater than or equal to one (1) to determine whether the first or next suffix array interval is valid.