Lempel-Ziv Parsing for Sequences of Blocks

The Lempel-Ziv parsing (LZ77) is a widely popular construction lying at the heart of many compression algorithms. These algorithms usually treat data as sequence bytes, i.e., blocks fixed length 8. Another common option to view bits. We investigate following natural question: what relationship between LZ77 parsings same interpreted fixed-length and bits (or other “elementary” letters)? In this paper, we prove that, for any integer b>1, number z phrases in string n zb which b are separate letters (e.g., b=8 case bytes) related zb=O(bzlognz). bound holds both “overlapping” “non-overlapping” versions LZ77. Further, establish tight zb=O(bz) special when each phrase has “phrase-aligned” earlier occurrence (an equal concatenation consecutive phrases). latter an important particular produced, instance, by grammar-based methods.