Some Classes of Quasi-Cyclic LDPC Codes: Properties and Efficient Encoding Method

Hachiro FUJITA  Kohichi SAKANIWA  

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E88-A   No.12   pp.3627-3635
Publication Date: 2005/12/01
Online ISSN: 
DOI: 10.1093/ietfec/e88-a.12.3627
Print ISSN: 0916-8508
Type of Manuscript: PAPER
Category: Coding Theory
Keyword: 
quasi-cyclic codes,  array codes,  LDPC codes,  encoder,  division circuit,  SFT codes,  Fossorier codes,  

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Summary: 
Low-density parity-check (LDPC) codes are one of the most promising next-generation error-correcting codes. For practical use, efficient methods for encoding of LDPC codes are needed and have to be studied. However, it seems that no general encoding methods suitable for hardware implementation have been proposed so far and for randomly constructed LDPC codes there have been no other methods than the simple one using generator matrices. In this paper we show that some classes of quasi-cyclic LDPC codes based on circulant permutation matrices, specifically LDPC codes based on array codes and a special class of Sridhara-Fuja-Tanner codes and Fossorier codes can be encoded by division circuits as cyclic codes, which are very easy to implement. We also show some properties of these codes.