Low-density parity-check codes based on finite geometries: A rediscovery and new results
Low-density parity-check codes based on finite geometries: A rediscovery and new results
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DOI：
10.1109/18.959255
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发表时间：
2001-11-01
影响因子：
2.5
通讯作者：
Fossorier, MPC
中科院分区：
文献类型：
--
作者：
Kou, Y;Lin, S;Fossorier, MPC
提出了一种构造低密度奇偶校验码（LDPC）的几何方法。基于有限域上欧氏几何和射影几何的直线和点构造了四类LDPC码。这四类码都有很好的最小距离，它们的坦纳图围长为6。几何LDPC码可以以各种方式解码，范围从低到高解码复杂度以及从相当好到非常好的性能。它们在迭代解码中表现得非常好。此外，它们可以以循环或准循环的形式存在。因此，它们的编码可以在线性时间内实现，并且可以用简单的反馈移位寄存器来实现。这一优点通常不为其他LDPC码所共享，并且在实践中是重要的。有限几何LDPC码可以通过各种方式进行扩展和缩短，以获得其他良好的LDPC码。提出了几种扩展和缩短的技术。长扩展有限几何LDPC码已经被构造出来，并且通过迭代解码，它们的性能距离香农理论极限仅零点几分贝。
This paper presents a geometric approach to the construction of low-density parity-check (LDPC) codes. Four classes of LDPC codes are constructed based on the lines and points of Euclidean and projective geometries over finite fields. Codes of these four classes have good minimum distances and their Tanner graphs have girth 6. Finite-geometry LDPC codes can be decoded in various ways, ranging from low to high decoding complexity and from reasonably good to very good performance. They perform very well with iterative decoding. Furthermore, they can be put in either cyclic or quasi-cyclic form. Consequently, their encoding can be achieved in linear time and implemented with simple feedback shift registers. This advantage is not shared by other LDPC codes in general and is important in practice. Finite-geometry LDPC codes can be extended and shortened in various ways to obtain other good LDPC codes. Several techniques of extension and shortening are presented. Long extended finite-geometry LDPC codes have been constructed and they achieve a performance only a few tenths of a decibel away from the Shannon theoretical limit with iterative decoding.