Use this URL to cite or link to this record in EThOS: http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.341388
Title: Statistical physics of error-correcting codes
Author: Vicente, Renato
Awarding Body: Aston University
Current Institution: Aston University
Date of Award: 2000
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Abstract:
In this thesis we use statistical physics techniques to study the typical performance of four families of error-correcting codes based on very sparse linear transformations: Sourlas codes, Gallager codes, MacKay-Neal codes and Kanter-Saad codes. We map the decoding problem onto an Ising spin system with many-spins interactions. We then employ the replica method to calculate averages over the quenched disorder represented by the code constructions, the arbitrary messages and the random noise vectors. We find, as the noise level increases, a phase transition between successful decoding and failure phases. This phase transition coincides with upper bounds derived in the information theory literature in most of the cases. We connect the practical decoding algorithm known as probability propagation with the task of finding local minima of the related Bethe free-energy. We show that the practical decoding thresholds correspond to noise levels where suboptimal minima of the free-energy emerge. Simulations of practical decoding scenarios using probability propagation agree with theoretical predictions of the replica symmetric theory. The typical performance predicted by the thermodynamic phase transitions is shown to be attainable in computation times that grow exponentially with the system size. We use the insights obtained to design a method to calculate the performance and optimise parameters of the high performance codes proposed by Kanter and Saad.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Phd
EThOS ID: uk.bl.ethos.341388  DOI: Not available
Keywords: Computer Science Signal processing Information theory Physics
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