标题： 基于群环的QC-LDPC码的构造与编码 显示英文标题

标题： Construction and Encoding of QC-LDPC Codes Using Group Rings

摘要： 准循环（QC）低密度奇偶校验（LDPC）码，即QC-LDPC码，由于可以通过循环移位寄存器实现简单的编码而被广泛应用。在本文中，我们从群环构造QC-LDPC码。群环是从任何给定的环和任何给定的群自然构造出的自由模（同时也是一个环）。我们提出了一种基于群环元素的结构，用于构造QC-LDPC码。一些之前用于构造基于有限域的QC-LDPC码的方法是所提出的构造方法的特例。所构造的QC-LDPC码在迭代解码下，在比特错误概率和块错误概率方面在加性高斯白噪声（AWGN）信道上表现非常好。仿真结果表明，与现有的类似LDPC码相比，所提出的码具有竞争力的性能。最后，我们提出了一种新的基于群环的QC-LDPC码的编码方法，该方法比当前的编码方法实现得更快。所提出方法的编码复杂度进行了数学分析，表明即使与现有的具有线性时间和空间复杂度的高效编码方法相比，所需的运算次数也显著减少。 显示英文摘要

摘要： Quasi-cyclic (QC) low-density parity-check (LDPC) codes which are known as QC-LDPC codes, have many applications due to their simple encoding implementation by means of cyclic shift registers. In this paper, we construct QC-LDPC codes from group rings. A group ring is a free module (at the same time a ring) constructed in a natural way from any given ring and any given group. We present a structure based on the elements of a group ring for constructing QC-LDPC codes. Some of the previously addressed methods for constructing QC-LDPC codes based on finite fields are special cases of the proposed construction method. The constructed QC-LDPC codes perform very well over the additive white Gaussian noise (AWGN) channel with iterative decoding in terms of bit-error probability and block-error probability. Simulation results demonstrate that the proposed codes have competitive performance in comparison with the similar existing LDPC codes. Finally, we propose a new encoding method for the proposed group ring based QC-LDPC codes that can be implemented faster than the current encoding methods. The encoding complexity of the proposed method is analyzed mathematically, and indicates a significate reduction in the required number of operations, even when compared to the available efficient encoding methods that have linear time and space complexities.