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An Introduction to Error-Correcting Codes
Published in Erozan M. Kurtas, Bane Vasic, Advanced Error Control Techniques for Data Storage Systems, 2018
[36,45] who observed that iterative decoding algorithms developed for these codes are instances of probability propagation algorithms operating on a graphical model of the code. The belief propagation algorithms and graphical models have been developed in the expert systems literature by Pearl [65] and Lauritzen and Spiegelhalter [45]. MacKay and Neal [48,58], and McEliece et al. [59] showed that Gallager’s algorithm [31] for decoding low-density parity-check codes proposed in the early 1960 s is essentially an instance of Pearl’s algorithm. Extensive simulation results of MacKay and Neal showed that Gallager codes could perform nearly as well as earlier developed turbo codes [6]. The same authors also observed that turbo decoding is an instance of “belief” propagation and provided a description of Pearl’s algorithm, and made explicit its connection to the basic turbo decoding algorithm described in [6]. The origins of the algorithm can be found in the work of Battail [3], Hartmann and Rudolph [35], Gallager [32] and Tanner [87].
Dynamic Forward Error Control Schemes
Published in Borko Furht, Syed Ahson, Handbook of Mobile Broadcasting, 2008
Besides turbo codes, another class of codes that turned out to approach Shannon’s bound, namely, low-density parity check codes (LDPC codes), were discovered by Robert Gallager in the 1960s. Like turbo codes, LDPC codes have an iterative decoder. The true power of these codes, however, was overlooked, due in part to the lack of sufficient computing power for their implementation at the time. Today, the codes coming closest to the Shannon bound are LDPC codes, and much work has recently been focused on their construction and analysis.
Coding Theory
Published in Leslie Hogben, Richard Brualdi, Anne Greenbaum, Roy Mathias, Handbook of Linear Algebra, 2006
Joachim Rosenthal, Paul Weiner
Low density parity check codes. A class of linear codes of tremendous practical importance was introduced by R.G. Gallager in his dissertation [Gal63]. These binary linear codes were called low density parity check (LDPC) codes by the author and are characterized by the property that the code can be written as the kernel of a very sparse matrix. For example, Gallager studied codes whose parity check matrix had three 1s in every column and six 1s in every row randomly chosen.
Iterative Threshold Channel Estimation in ORGV Convolutional Code MISO-OFDM System
Published in IETE Technical Review, 2022
Xiao Zhou, Mingtong Zhang, Chengyou Wang
STBC, SFBC, and STFBC are constructed according to the orthogonal design principle of codewords. Convolutional code can be considered as an effective technology of channel coding to improve the performance of OFDM system. Combining SFBC with convolutional code is an efficient technology to combat antenna interference. The low density parity check code (LDPC) is comparatively easy to construct, therefore it is used in 5G, wireless fidelity (Wi-Fi), and world interoperability for microwave access (WiMAX). Moreover, LDPC is widely used in the hardware of the multiple-input multiple-output OFDM (MIMO-OFDM) systems.