Low Complexity Encoding Based on Richardson's LDPC Codes

Hyunseuk YOO  Chang Hui CHOE  Moon Ho LEE  

IEICE TRANSACTIONS on Communications   Vol.E90-B   No.8   pp.2151-2154
Publication Date: 2007/08/01
Online ISSN: 1745-1345
DOI: 10.1093/ietcom/e90-b.8.2151
Print ISSN: 0916-8516
Type of Manuscript: LETTER
Category: Fundamental Theories for Communications
finite fields,  circulant permutation matrices,  Richardson's encoding scheme,  computational complexity,  

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The key weakness of Low-Density Parity Check codes is the complexity of the encoding scheme. The generator matrices can be made by Gaussian elimination of parity check matrices for normal block codes. Richardson succeeded in making parity bits from parity check matrices by the low density computation. In this letter, we focus on the execution of numerical experiments which show that even if the matrix D, which is the part of the Richardson's LDPC matrix, is restricted, proposed LDPC codes is lower complexity than Richardson's LDPC codes. The constraint of D results in reducing complexity from O(n + g2) to O(n) due to the omission of computing inverse matrices of φ and T in Richardson's encoding scheme. All the sub-matrices in parity check matrix are composed of Circulant Permutation Matrices based on Galois Fields.