Adaptive Methods for Linear Programming Decoding
Taghavi, M.-H.N.
Siegel, P.H.
Dept. of Electr. & Comput. Eng., Univ. of California, La Jolla, CA;
This paper appears in: Information Theory, IEEE Transactions on
Publication Date: Dec. 2008
Volume: 54,
Issue: 12
On page(s): 5396-5410
ISSN: 0018-9448
INSPEC Accession Number: 10324579
Digital Object Identifier: 10.1109/TIT.2008.2006384
Current Version Published: 2008-11-25
Abstract
Detectability of failures of linear programming (LP) decoding and the potential for improvement by adding new constraints motivate the use of an adaptive approach in selecting the constraints for the underlying LP problem. In this paper, we make a first step in studying this method, and show that by starting from a simple LP problem and adaptively adding the necessary constraints, the complexity of LP decoding can be significantly reduced. In particular, we observe that with adaptive LP decoding, the sizes of the LP problems that need to be solved become practically independent of the density of the parity-check matrix. We further show that adaptively adding extra constraints, such as constraints based on redundant parity checks, can provide large gains in the performance.
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