Improved LZ77 Compression with Match-Length-Dependent Sliding Windows

We devise and analyze WLZ, a family of LZ77 encoders whose sliding-window sizes depend on match length: short matches use smaller windows and shorter distance fields, while long matches retain access to distant repetitions. Write $B:=\log_2 W$ for the maximum window $W$. A parsing-transfer bound charges both window restrictions and missed matches, preserving established convergence and finite-input minimax orders, and a sharper block charge proves stationary-ergodic universality of exact greedy WLZ when full-window matching begins at length $o(B)$. A calibrated window schedule never increases minimum token cost relative to a single-window baseline and saves $Ω(BW^{-β})$ in rate on specified iid sources, with $β>2$. The remaining gains come from the token code rather than the windows. On a uniform iid source, a growing phrase cap with a cheap length symbol improves redundancy from the $Ω(\log B/B)$ of the original 1977 fixed-field format, whatever phrase cap it uses, to $O(\log\log B/B)$. Recoding a single-symbol run $(r,1)$ as $(1,r)$, with a logarithmic-cost count $r$ that may exceed the match cap, codes inputs with $O(n^α)$ runs, $0\leα<1$, in $O(n^α\log n)$ bits, versus $Ω(n)$ for that format with phrase cap $Θ(\log W)$ and $W=o(n)$. On globally $p$-periodic inputs, Huffman coding the fields of a capped parse with nearest-distance ties reduces the large-file rate from $Θ(B/W)$ under fixed-width coding to at most $3/W$, including tables and framing. Finally, selection among complete WLZ codes yields an entropy-rate estimator consistent almost surely and in mean, with finite-data error bounds for fixed nonuniform iid sources.