The Symmetries of Mappings of Bit-interleaved Coded Modulation (with Iterative Decoding) Systems and Its Applications

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.