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          "citation": "Jacob Ziv and Abraham Lempel, Compression of Individual Sequences via Variable-Rate Coding, IEEE Transactions on Information Theory 24(5), 530–536 (1978), DOI 10.1109/TIT.1978.1055934",
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      "statement": "# Ziv and Lempel: individual-sequence variable-rate lossless coding\n\nThe paper defines compressibility for an individual infinite sequence against finite-state information-lossless encoders and gives an incremental-parsing coding construction that asymptotically attains that benchmark without a specified probabilistic source.\n\nThe decoder preserves the original symbols exactly. New phrases combine an earlier phrase with a new symbol, supporting the construction associated with LZ78. Converse bounds explain the finite-state benchmark; a separate theorem connects it to entropy for ergodic sources.\n\n## Scientific scope\n\nThe target is the 1978 paper's finite-alphabet, finite-state lossless setting. Its state-count and input-length limits retain their stated order; a family with growing block length is not one fixed machine that compresses every finite input optimally. LZ 77, later dictionary formats and lossy coding remain distinct. The paper's proof was read but not independently reconstructed or formally replayed.\n\n## People and systems\n\nJacob Ziv; Abraham Lempel\n\n\n\n## Original sources\n\n- [Jacob Ziv and Abraham Lempel, Compression of Individual Sequences via Variable-Rate Coding, IEEE Transactions on Information Theory 24(5), 530–536 (1978), DOI 10.1109/TIT.1978.1055934](https://www.philippe-fournier-viger.com/spmf/lz78.pdf)\n- [DBLP bibliographic record for Ziv and Lempel, 1978 variable-rate coding paper](https://dblp.org/rec/journals/tit/ZivL78)\n",
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