Decoding Binary Linear Block Codes Using Local Search

This paper presents a novel iterative hard decision decoding algorithm for binary linear block codes over a binary symmetric channel (BSC). The problem is formulated as a 0-1 integer programming problem which is known to be NP-hard. When the crossover probability c of the channel is known, the solut...

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Bibliographic Details
Published in:IEEE transactions on communications Vol. 61; no. 6; pp. 2138 - 2145
Main Authors: Esmaeili, M., Alampour, A., Gulliver, T. A.
Format: Journal Article
Language:English
Published: New York, NY IEEE 01.06.2013
Institute of Electrical and Electronics Engineers
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Algorithm design and analysis
Algorithms
Applied sciences
Coding, codes
Exact sciences and technology
Indexes
Information, signal and communications theory
Integer programming
Integer programming decoding
Iterative decoding
Linear programming
Maximum likelihood decoding
maximum likelihood hard decision decoding
multi-flip local search decoding
Search problems
Signal and communications theory
Studies
Telecommunications and information theory
Performance evaluation
Block code
Binary channel
multi-flip local search decoding
Probabilistic approach
Cross-over phenomenon
Code distance
Iterative method
Binary code
Iterative decoding
Penalty method
Search algorithm
Integer programming
Linear code
Penalty function
Credal approach
NP hard problem
maximum likelihood hard decision decoding
Numerical simulation
Minimal distance
Maximum likelihood
Integer programming decoding
ISSN:0090-6778, 1558-0857
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Description
Summary:This paper presents a novel iterative hard decision decoding algorithm for binary linear block codes over a binary symmetric channel (BSC). The problem is formulated as a 0-1 integer programming problem which is known to be NP-hard. When the crossover probability c of the channel is known, the solution space of the decoding problem can be decreased to a sphere whose radius is related to c. Using the penalty function method, the problem is reformulated on this reduced solution space. Then an iterative multi-flip local search algorithm is designed to find the global solution of this decoding problem. For a code with minimum distance d, when the radius of the sphere is not greater than d-1/2, this algorithm has the maximum likelihood (ML) certificate property, i.e., if the decoder outputs a codeword, it is guaranteed to be the ML codeword. Compared to the probabilistic suboptimal iterative belief propagation (BP) decoder, this approach has lower complexity and better performance. Numerical results show that in terms of speed and performance the proposed decoding method outperforms BP decoding in the error floor region.
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ISSN:0090-6778
1558-0857
DOI:10.1109/TCOMM.2013.041113.120057