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### A class of quasi-cyclic LDPC codes and encoding

Xia Guojiang; Qi Jianzhong; Sun Huixian; Xiong Weiming

• Received:1900-01-01 Revised:1900-01-01 Online:2009-07-15 Published:2009-07-15

Abstract: Firstly, based on the characters of space communication, this study improves a class of regular quasi-cyclic LDPC codes which is based on circulant matrices and obtains a kind of irregular quasi-cyclic LDPC codes. Compared with original codes, the parity check matrix called H of this irregular LDPC ensemble has three characters: 1. $\pmb H$ is row full rank; 2. H is lower triangulation; 3. $\pmb H$ contains degree one variable nodes. With the first two characters, the encoding complexity of computation and architecture of this kind of LDPC are proportion to the length of check symbols, so encoders implemented with software and hardware are quite simple. This feature is very important to deep space communication because the resource on board is constrained. The third character makes the iterative decoding threshold lower than the original codes. Moreover, the computer simulation has proved this result. Secondly, the proof for the condition of girth not shorter than 6 is simplifed compared to the original ones. Last, the computing formula is derived for parity check symbols of systemic codes. Based on this formula, the encoding circuit has been investigated using shift registers.

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