SWhat changed
Couples a regular sparse code ensemble and typical-distance/error analysis with local soft-information iterative decoding, explicitly distinguishing tree-valid inference from later-cycle approximation.
Scientific scope
Couples a regular sparse code ensemble and typical-distance/error analysis with local soft-information iterative decoding, explicitly distinguishing tree-valid inference from later-cycle approximation. The original work defines sparse parity-check ensembles and a specified iterative decoding procedure. Its channel, independence/tree-like neighborhood and limiting assumptions matter. Ensemble averages are not per-code finite-block guarantees, and cycles can affect iterative behavior. Later capacity-approaching irregular codes, decoding variants and communications deployments retain separate credit.
Evidence
Source-linked, scoped account of the original work. The published scope states the scientific assumptions and remaining verification limits. WRS has not independently certified the full proof, experimental result or system benchmark.
Contributors
- Robert G. Gallager · SCIENCE: Original source-listed scientific author of this scoped work; byline does not determine effort fractions.
- R. G. Gallager, Low-Density Parity-Check Codes, IRE Transactions on Information Theory IT-8(January 1962),21–28
- Gallager's MIT-hosted bibliography:1962 low-density parity-check article
Provisional WRS assessment, edition 2026-10-16.1. Independent expert calibration is pending. This grade does not certify correctness or assign ownership.
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