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Advanced Coding for Fiber-Optics Communications Systems
Published in Andrew Ellis, Mariia Sorokina, Optical Communication Systems, 2019
The most obvious way to design LDPC codes is to construct a low-density parity-check matrix with prescribed properties. Some important LDPC designs, among others, include: Gallager codes (semi-random construction) [31], MacKay codes (semi-random construction) [32], combinatorial design-based LDPC codes [33] (see [34] for combinatorial designs), finite-geometry-based LDPC codes [35, 36], array [also known as quasi-cyclic (QC)] LDPC codes [37, 38], to mention a few. The generator matrix of a QC-LDPC code can be represented as an array of circulant sub-matrices of the same size B indicating that QC-LDPC codes can be encoded in linear time using simple shift-register-based architectures [39]. A QC-LDPC code can be defined as an LDPC code for which every sectional cyclic shift to the right (or left) for l ∈ [0, B−1] places of a codeword v = [v0v1 … vB−1] (each section vi contains B elements) results in another codeword.
Security in Wireless Sensor Networks
Published in Shafiullah Khan, Al-Sakib Khan Pathan, Nabil Ali Alrajeh, Wireless Sensor Networks, 2016
Cametepe et al. have proposed a deterministic key distribution scheme for WSNs using combinatorial design theory [91]. The combinatorial design theory–based pairwise key predistribution (CDTKeying) scheme is based on block design techniques in combinatorics. It uses symmetric and generalized quadrangle design techniques. The scheme uses a finite projective plane of order n (for prime power of n) to generate a symmetric design with parameters n2 + n + 1, n + 1, and 1. The design supports n2 + n + 1 nodes and uses a key pool of size n2 + n + 1. It generates n2 + n + 1 key chains of size n + 1 in which every pair of key chains has exactly one key in common, and every key appears in exactly n + 1 key chains. After deployment, every pair of nodes finds exactly one common key. Thus, the probability of key sharing among a pair of sensor nodes is unity. The disadvantage of this proposition is that the parameter n has to be a prime power. Therefore, all network sizes can be supported for a fixed key chain size.
Security in Wireless Sensor Networks
Published in Yan Zhang, Jun Zheng, Honglin Hu, Security in Wireless Mesh Networks, 2008
Yong Wang, Garhan Attebury, Byrav Ramamurthy
Camtepe and Yener proposed a deterministic key distribution scheme for WSNs using Combinatorial Design Theory [65]. The Combinatorial Design Theory based pairwise key pre-distribution (CDTKeying) scheme is based on block design techniques in combinatorial design theory. It employs symmetric and generalized quadrangle design techniques. The scheme uses a finite projective plane of order n (for prime power n) to generate a symmetric design with parameters n2 + n + 1, n + 1, 1. The design supports n2 + n + 1 nodes and uses a key pool of size n2 + n + 1. It generates n2 + n + 1 key chains of size n + 1 where every pair of key chains has exactly one key in common, and every key appears in exactly n + 1 key-chains. After the deployment, every pair of nodes finds exactly one common key. Thus, the probability of key sharing among a pair of sensor nodes is 1. The disadvantage of this solution is that the parameter n has to be a prime power, thus indicating that not all network sizes can be supported for a fixed key chain size.
A Scalable Key Pre-distribution Scheme based on the Unital Design for the Internet of Things Security
Published in IETE Journal of Research, 2023
V. Chegeni, H. Haj Seyyed Javadi, M.R. Moazami Goudarzi, A. Rezakhani
Combinatorial design theory deals with the arrangement of elements into subsets satisfying some generalized concepts of balance and symmetry. The focus here is primarily on the definition and properties of a particular kind of design, namely the Balanced Incomplete Block Designs (BIBD), and symmetric BIBD.