Exact Separation of Forbidden-Set Cuts Associated With Redundant Parity Checks of Binary Linear Codes

In recent years, several integer programming (IP) approaches were developed for maximum-likelihood decoding and minimum distance computation for binary linear codes. Two aspects in particular have been demonstrated to improve the performance of IP solvers as well as adaptive linear programming decod...

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Published in:IEEE communications letters Vol. 24; no. 10; pp. 2096 - 2099
Main Authors: Puchert, Christian, Tillmann, Andreas M.
Format: Journal Article
Language:English
Published: New York IEEE 01.10.2020
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Binary codes
Binary system
Codes
Computational complexity
Computational modeling
Decoders
Hamming weight
Indexes
integer linear programming
Integer programming
IP networks
Linear codes
Linear programming
Maximum likelihood decoding
Optimization
Parity
Parity check codes
Separation
Solvers
ISSN:1089-7798, 1558-2558
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Abstract In recent years, several integer programming (IP) approaches were developed for maximum-likelihood decoding and minimum distance computation for binary linear codes. Two aspects in particular have been demonstrated to improve the performance of IP solvers as well as adaptive linear programming decoders: the dynamic generation of forbidden-set (FS) inequalities, a family of valid cutting planes, and the utilization of so-called redundant parity-checks (RPCs). However, to date, it had remained unclear how to determine whether or not there exists any violated FS inequality w.r.t. any known or unknown parity-check. In this note, we prove NP -hardness of this RPC separation problem. Moreover, we formulate an IP model that combines the search for most violated FS cuts with the generation of RPCs, and report on computational experiments. Empirically, for various instances of the minimum distance problem, it turns out that while utilizing the exact separation IP does not appear to provide a computational advantage, it can apparently be avoided altogether by combining heuristics to generate RPC-based cuts.
AbstractList In recent years, several integer programming (IP) approaches were developed for maximum-likelihood decoding and minimum distance computation for binary linear codes. Two aspects in particular have been demonstrated to improve the performance of IP solvers as well as adaptive linear programming decoders: the dynamic generation of forbidden-set (FS) inequalities, a family of valid cutting planes, and the utilization of so-called redundant parity-checks (RPCs). However, to date, it had remained unclear how to determine whether or not there exists any violated FS inequality w.r.t. any known or unknown parity-check. In this note, we prove NP -hardness of this RPC separation problem. Moreover, we formulate an IP model that combines the search for most violated FS cuts with the generation of RPCs, and report on computational experiments. Empirically, for various instances of the minimum distance problem, it turns out that while utilizing the exact separation IP does not appear to provide a computational advantage, it can apparently be avoided altogether by combining heuristics to generate RPC-based cuts.
Author Tillmann, Andreas M.
Puchert, Christian
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SubjectTerms Binary codes
Binary system
Codes
Computational complexity
Computational modeling
Decoders
Hamming weight
Indexes
integer linear programming
Integer programming
IP networks
Linear codes
Linear programming
Maximum likelihood decoding
Optimization
Parity
Parity check codes
Separation
Solvers
Title Exact Separation of Forbidden-Set Cuts Associated With Redundant Parity Checks of Binary Linear Codes
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