Access Pattern Problem

I need to traverse a gigantic array of characters by a sliding window of length w, with offset of just 1 character. For quite a while, I still can not figure out a good access pattern which has the least latency for using a bunch of threads, each of which deals with a sequence window of w characters.

I made some sort of compression on the characters, because a word can have 4 characters contained in one unit.

ABCD DCBA ABDC DABC…
|-----w----|
–>sliding

i.e. Thread 0 takes care of ABCDD, and Thread 1 takes care of BCDDC.

Thanks