Coding Theory

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7 domain-specific abstractions whose origin domain is Coding Theory.

• Algebraic geometry code — An error-correcting linear code obtained by evaluating functions or taking residues on rational points of an algebraic curve over a finite field.
• Elias Bassalygo bound — An asymptotic upper bound on error-correcting-code rate derived by restricting codewords to a dense Hamming sphere and applying a Plotkin-type distance bound.
• Linear programming decoding — Error-correcting-code decoding by relaxing maximum-likelihood integer constraints to a tractable linear program over a codeword polytope approximation.
• Parvaresh–Vardy code — An algebraic error-correcting code that encodes correlated polynomial evaluations so received words can be efficiently list-decoded beyond the Reed–Solomon radius.
• Polar code (coding theory) — A linear error-correcting code that recursively transforms channels into nearly perfect and nearly useless bit-channels, placing information only on the reliable ones.
• Sequential decoding — A variable-effort tree-search method for approximately maximum-likelihood decoding long convolutional or tree codes using far less memory than exhaustive trellis decoding.
• Wozencraft ensemble — An explicit finite ensemble of rate-one-half linear codes over a finite field in which almost every member asymptotically meets the Gilbert–Varshamov distance bound.