John, you know much coding theory much better than I do so I am inclinced to defer to your superior knowledge...
Now behold the awesome power of gpt-Pro
Let’s unpack the question in pieces:
1. Is ZIP (a.k.a. DEFLATE) “locally decodable” or not?
Standard ZIP files are typically not “locally decodable” in the strictest sense—i.e., you cannot start decoding exactly at the byte corresponding to your region of interest and reconstruct just that portion without doing some earlier decoding.
The underlying method, DEFLATE, is indeed based on LZ77 plus Huffman coding. LZ77 uses back‐references to prior segments of the uncompressed data, which forces you to at least partially decode from an earlier point to resolve those references.
However, many ZIP files are stored in blocks or chunks—sometimes called “deflate blocks.” So if you only need data near the start of a block (rather than in the middle of one), you can skip previous blocks and just decode that chunk. Still, you cannot trivially jump to an arbitrary byte offset inside the block without re-initializing the LZ77 state from somewhere earlier.
2. If ZIP is “based on Lempel–Ziv,” can we easily modify it for local decodability?
Because Lempel–Ziv (LZ) methods revolve around referencing earlier uncompressed substrings, one must store enough information (or replicate the references with separate “partial dictionaries”) if one wants truly local decodability.
One can certainly modify an LZ-based compression scheme so that each block is smaller, or that references never cross block boundaries, etc. That would allow a more local decoding property: you only decode from the start of the local block rather than from the entire file.
This usually comes with tradeoffs. If your blocks are small, you lose compression efficiency because you can’t take advantage of references bridging across large swaths of data. So making a compression format “locally decodable” in a fine‐grained way often lowers the overall compression ratio.
3. Is Lempel–Ziv (and thus ZIP) lossless?
Yes. Standard LZ77 (or LZ78, LZMA, etc.) is a lossless compression scheme: you can reconstruct the exact original data bit for bit. The DEFLATE algorithm used in ZIP is also lossless.
4. Does the picture change when doing lossy compression?
Yes, quite a bit. In lossy compression (like JPEG for images or MP3/AAC for audio), parts of the original data are thrown away. Often you can still decode small “chunks” of the file—e.g., many lossy audio or video formats do decode in frames or segments. But the format internals (e.g., DCT coefficients in JPEG, wavelet transforms, etc.) differ a lot from LZ-based bit-by-bit exactness.
In lossy formats that use transform blocks (like 8×8 pixel blocks in JPEG), you can decode each block locally, but you still have boundary effects, optional overlap between blocks, etc. So “local decodability” there can be simpler in some ways (each block is more independent), but it’s also less “exact” because we accept errors from the original data.
Short Summary
ZIP/DEFLATE is not strictly locally decodable because LZ77 references require that you decode from (at least) the beginning of the current block.
You can modify an LZ-based scheme (for instance, by using smaller blocks or restricting cross‐block references) to make it more locally decodable, but that typically sacrifices some compression ratio.
LZ methods and ZIP are lossless.
With lossy compression, “local decodability” can be easier in the sense that each block may be decoded without referencing data too far outside itself—but at the cost that you’re not reconstructing the original data exactly.
John, you know much coding theory much better than I do so I am inclinced to defer to your superior knowledge...
Now behold the awesome power of gpt-Pro