Adaptive Cut Generation Algorithm for Improved Linear Programming Decoding of Binary Linear Codes

Linear programming (LP) decoding approximates maximum-likelihood (ML) decoding of a linear block code by relaxing the equivalent ML integer programming (IP) problem into a more easily solved LP problem. The LP problem is defined by a set of box constraints together with a set of linear inequalities...

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Vydáno v:IEEE transactions on information theory Ročník 58; číslo 10; s. 6581 - 6594
Hlavní autoři: Xiaojie Zhang, Siegel, P. H.
Médium: Journal Article
Jazyk:angličtina
Vydáno: New York, NY IEEE 01.10.2012
Institute of Electrical and Electronics Engineers
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Témata:
Algorithm design and analysis
Algorithms
Applied sciences
Approximation
Block codes
Codes
Coding theory
Coding, codes
Decoders
Decoding
Exact sciences and technology
Inequalities
Information theory
Information, signal and communications theory
Iterative decoding
linear codes
Linear programming
linear programming (LP) decoding
Low density parity check codes
low-density parity-check (LDPC) codes
Matrix
Maximum likelihood decoding
Maximum likelihood method
maximum-likelihood (ML) decoding
Parity
pseudocodewords
Signal and communications theory
Simulation
Telecommunications and information theory
Vectors
Performance evaluation
Block code
linear codes
Adaptive algorithm
Error estimation
Error rate
Iterative method
maximum-likelihood (ML) decoding
Binary code
Adaptive method
pseudocodewords
Iterative decoding
Linear code
low-density parity-check (LDPC) codes
Parity check codes
Linear programming
Maximum likelihood decoding
Integer programming
Necessary condition
linear programming (LP) decoding
Sufficient condition
Simulation
Hypercube
Error correcting code
Parity check
ISSN:0018-9448, 1557-9654
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Popis
Shrnutí:Linear programming (LP) decoding approximates maximum-likelihood (ML) decoding of a linear block code by relaxing the equivalent ML integer programming (IP) problem into a more easily solved LP problem. The LP problem is defined by a set of box constraints together with a set of linear inequalities called "parity inequalities" that are derived from the constraints represented by the rows of a parity-check matrix of the code and can be added iteratively and adaptively. In this paper, we first derive a new necessary condition and a new sufficient condition for a violated parity inequality constraint, or "cut," at a point in the unit hypercube. Then, we propose a new and effective algorithm to generate parity inequalities derived from certain additional redundant parity check (RPC) constraints that can eliminate pseudocodewords produced by the LP decoder, often significantly improving the decoder error-rate performance. The cut-generating algorithm is based upon a specific transformation of an initial parity-check matrix of the linear block code. We also design two variations of the proposed decoder to make it more efficient when it is combined with the new cut-generating algorithm. Simulation results for several low-density parity-check (LDPC) codes demonstrate that the proposed decoding algorithms significantly narrow the performance gap between LP decoding and ML decoding.
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ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2012.2204955