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An Efficient Method to Construct Parity-Check Matrices for Recursively Encoding Spatially Coupled LDPC Codes †

Key Laboratory of Universal Wireless Communications, Ministry of Education, Beijing University of Posts and Telecommunications (BUPT), No. 10 Xitucheng Road, Haidian District, Beijing 100876, China
*
Author to whom correspondence should be addressed.
This paper is an extended version of our paper published in the 2015 IEEE International Symposium on Personal, Indoor and Mobile Radio Communications, Hong Kong, China, 30 August–2 September 2015.
Academic Editor: Raúl Alcaraz Martínez
Entropy 2016, 18(8), 305; https://doi.org/10.3390/e18080305
Received: 15 June 2016 / Revised: 23 July 2016 / Accepted: 15 August 2016 / Published: 17 August 2016
(This article belongs to the Section Information Theory, Probability and Statistics)
Spatially coupled low-density parity-check (LDPC) codes have attracted considerable attention due to their promising performance. Recursive encoding of the codes with low delay and low complexity has been proposed in the literature but with constraints or restrictions. In this manuscript we propose an efficient method to construct parity-check matrices for recursively encoding spatially coupled LDPC codes with arbitrarily chosen node degrees. A general principle is proposed, which provides feasible and practical guidance for the construction of parity-check matrices. According to the specific structure of the matrix, each parity bit at a coupling position is jointly determined by the information bits at the current position and the encoded bits at former positions. Performance analysis in terms of design rate and density evolution has been presented. It can be observed that, in addition to the feature of recursive encoding, selected code structures constructed by the newly proposed method may lead to better belief-propagation thresholds than the conventional structures. Finite-length simulation results are provided as well, which verify the theoretical analysis. View Full-Text
Keywords: channel coding; spatially coupled LDPC codes; protograph codes; recursive encoding; density evolution channel coding; spatially coupled LDPC codes; protograph codes; recursive encoding; density evolution
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MDPI and ACS Style

Si, Z.; Wang, S.; Ma, J. An Efficient Method to Construct Parity-Check Matrices for Recursively Encoding Spatially Coupled LDPC Codes †. Entropy 2016, 18, 305.

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