Abstract
The natural Hilbert Space of quantum particles can implement maximum-likelihood (ML) decoding of classical information. The “Quantum Product Algorithm” (QPA) is computed on a Factor Graph, where function nodes are unitary matrix operations followed by appropriate quantum measurement. QPA is like the Sum-Product Algorithm (SPA), but without summary, giving optimal decode with exponentially finer detail than achievable using SPA. Graph cycles have no effect on QPA performance. QPA must be repeated a number of times before successful and the ML codeword is obtained only after repeated quantum “experiments”. ML amplification improves decoding accuracy, and Distributed QPA facilitates successful evolution.
Résumé
L’espace de Hilbert naturel des particules quantiques permet l’implémentation du décodage suivant le Maximum de Vraisemblance (MV) des codes classiques. L’Algorithme de Produit Quantique (APQ) est calculé sur un graphe de dépendance où les fonctions sur les nceuds sont dèfinies par des matrices unitaires suivies par une mesure quantique appropriée. L’APQ est similaire à l’Algorithme Somme-Produit (ASP), sans la sommation, avec un décodage optimal donnant une plus grande précision que celle fournie par l’ASP. Les cycles dans les graphes n’affectent pas les performances de l’APQ. L’APQ doit être répété plusieurs fois pour aboutir au résultat et le mot de code optimal suivant le MV est obtenu uniquement après plusieurs tentatives de l’expérience quantique. L’amplification du MV améliore la précision de décodage et l’APQ distribué facilite la convergence.
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This work was funded by NFR Project Number 119390/431, and was presented in part at 2nd Int. Symp. on Turbo Codes and Related Topics, Brest, Sept. 4–7, 2000
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Parker, M.G. Quantum factor graphs. Ann. Télécommun. 56, 472–483 (2001). https://doi.org/10.1007/BF02995457
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DOI: https://doi.org/10.1007/BF02995457