比特交织编码调制(迭代译码)系统标识映射的对称性研究与应用
doi: 10.3724/SP.J.1146.2013.00382
The Symmetries of Mappings of Bit-interleaved Coded Modulation (with Iterative Decoding) Systems and Its Applications
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摘要: 该文从群论的角度分析了比特交织编码调制(迭代译码)(BICM(-ID))系统中标识映射的对称性。首先给出了标识映射对称性的定义，并指出，二进制标识映射的对称性是BICM(-ID)系统的固有特性，该对称性同构于m阶超立方的对称群。然后基于BICM(-ID)的对称性，提出一种改进的二进制交换算法(IBSA)。该算法的搜索空间为标识映射对称群陪集的代表系。因此，与传统的二进制算法相比，IBSA的搜索效率得到了提高。最后，2维16阶星座图的仿真结果表明，在40000次的运行过程中，IBSA能提高4%的搜索效率；32阶相移键控星座图的仿真结果表明，该算法至少可提高3.5%的搜索效率，单个映射的计算时间缩短了约4000倍。Abstract: Based on the group theory, the symmetries of mappings of Bit-Interleaved Coded Modulation (or with Iterative Decoding) systems (BICM(-ID)) are studied. Firstly, the definitions of the symmetries of mappings for BICM (-ID) are given. The symmetries of binary labels of a mapping are the intrinsic properties of BICM(-ID), which are isomorphic to the symmetry group of a hypercube of order m. According to the symmetries of BICM (-ID), an Improved Binary Switch Algorithm (IBSA) is proposed. The search space of IBSA is a transversal of the symmetry group of mappings. Consequently, the efficiency of IBSA is improved compared to the traditional BSA. Finally, Simulation results of a 16-ary two dimensional constellation show that the search efficiency of IBSA can be improved about 4% during 40000 trials. For 32-PSK, the results show that the search efficiency can be improved at least 3.5% and the time required to calculate a single mapping is shorten about 4000 times.
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