Low Complexity Encoder for Generalized Quasi-Cyclic Codes Coming from Finite Geometries
Low Complexity Encoder for Generalized Quasi-Cyclic Codes Coming from Finite Geometries
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DOI：
10.1109/icc.2009.5199152
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发表时间：
2009-06
期刊：
影响因子：
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通讯作者：
V. Van;H. Matsui;S. Mita
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文献类型：
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作者：
V. Van;H. Matsui;S. Mita
我们定义广义准循环（GQC）码为具有非平凡自同构群的线性码。因此，GQC码，不像准循环码，可以包括许多重要的代码，如埃尔米特和投影几何（PG）码;这种能力是重要的，在实际应用中。此外，我们提出了梯队标准形算法计算Grobner基地从他们的奇偶校验矩阵。因此，应用Grobner基理论，GQC码可以用简单的反馈移位寄存器系统地编码和实现。我们的算法是基于高斯消除，并需要一个足够小的数量有限域操作，这是有关的三次幂的码长。为了证明我们的编码器的效率，我们证明了编码器架构中的电路元件的数量是成比例的有限几何（FG）LDPC码（一类GQC码）的码长。我们表明，FG-LDPC码的串行输入串行输出编码器架构的硬件复杂度与码长的线性顺序有关;编码长度为n的二进制码字需要少于2n个加法器和2n个存储器元件。
We define generalized quasi-cyclic (GQC) codes as linear codes with nontrivial automorphism groups. Therefore, GQC codes, unlike quasi-cyclic codes, can include many important codes such as Hermitian and projective geometry (PG) codes; this capability is important in practical applications. Further, we propose the echelon canonical form algorithm for computing Grobner bases from their parity check matrices. Consequently, by applying Grobner base theory, GQC codes can be systematically encoded and implemented with simple feedback shift registers. Our algorithm is based on Gaussian elimination and requires a sufficiently small number of finite-field operations, which is related to the third power of code-length. In order to demonstrate our encoder's efficiency, we prove that the number of circuit elements in the encoder architecture is proportional to the code-length for finite geometry (FG) LDPC codes (a class of GQC codes). We show that the hardware complexity of a serial-in-serial-out encoder architecture for FG-LDPC codes is related to the linear order of the code-length; less than 2n adder and 2n memory elements are required to encode a binary codeword of length n.