基于有限域的LDPC卷积码构造算法

采用有限域方法研究获得具有快速编码特性的规则、时不变LDPC（Low-Density Parity-Check，低密度奇偶校验）卷积码的构造算法. 首先给出基于有限域GF(q)所构造的准循环(QC)LDPC码的基矩阵结构特性；然后提供了一种新的代数构造及其对应的修正的矩阵结构；最后，根据QC与LDPC卷积码之间的环同构关系，获得了具有快速编码特性的LDPC卷积码的多项式矩阵结构. 代数构造方法简化了整个构造过程. 而LDPC卷积码的快速编码特性减小了编码复杂度，简化了编码器结构. 用基于置信传播(BP)的译码算法在加性高斯白噪声(AWGN)信道上获得的仿真结果表明，与其他结构化LDPC卷积码相比，文中所构造的码具有更好的性能.

Construction of LDPC Convolutional Codes Based on Finite Fields

〖JP2〗A new algebraic construction of regular, time-invariant low-density parity-check (LDPC) convolutional codes with fast encoding based on finite fields is proposed in this paper. 〖JP2〗It is first specified the structure properties of a base matrix which is associated with a〖JP〗 quasi-cyclic (QC) LDPC code constructed based on finite fields GF(q). A concrete algebraic construction and its modified form of the matrix are then given. Finally, according to the ring isomorphism relationship between a QC code and a convolutional LDPC code, the polynomial 〖JP〗matrix corresponding to an LDPC convolutional code with fast encoding is developed. The algebraic construction simplifies the construction process significantly. In particular, the fast encoding property can both reduce the encoding complexity and simplify encoder structure. Simulation results show that the proposed LDPC convolutional codes have more excellent performance in comparison with the existing counterparts under belief propagation (BP) decoding algorithm over additive Gaussian white noise (AWGN) channels.