SIAM Journal on Applied Mathematics · 1979 · 192 citations · 5 references
EngineeringJoint Source-channel CodingCoding TheorySoft Decoding TechniquesError Correction CodePolar CodesConvolutional DecodingIterative DecodingComputer ScienceConvolutional CodesDeep LearningSignal ProcessingTurbo CodesVariable-length CodeAlgebraic Coding Theory
Convolutional codes of any rate and constraint length generate quasi‑cyclic codes, and every quasi‑cyclic code can be convolutionally encoded; this includes quadratic residue, Reed–Solomon, and optimal BCH codes. The authors determine the constraint length K needed to convolutionally encode many of these codes, such as Golay and the (48,24) OR code. The resulting constraint lengths are surprisingly small, allowing soft‑decoding convolutional techniques to yield a new maximum‑likelihood decoding algorithm for many block codes, and demonstrating that optimal quasi‑cyclic codes produce convolutional encodings with optimal local and favorable infinite‑length properties.
Convolutional codes of any rate and any constraint length give rise to a sequence of quasi-cyclic codes. Conversely, any quasi-cyclic code may be convolutionally encoded. Among the quasi-cyclic codes are the quadratic residue codes, Reed–Solomon codes and optimal BCH codes. The constraint length K for the convolutional encoding of many of these codes (Golay, (48, 24) OR, etc.) turns out to be surprisingly small. Thus using the soft decoding techniques for convolutional decoding we now have a new maximum likelihood decoding algorithm for many block codes. Conversely an optimal quasi-cyclic code will yield a convolutional encoding with optimal local properties and therefore with good infinite convolutional coding properties.
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