A coded modulation scheme for 64-QAM with a matched mapping

A well known trellis coded modulation using a set partitioning has a shortcoming. Even if a powerful error correcting code is applied to the coded modulation, the smallest squared Euclidean distance between different coded sequences can not exceed the minimum squared Euclidean distance between pairwise signal points mapped by uncoded information bits in any one of the subsets. Ring convolutional codes over rings of integers modulo M without using a set partitioning have been proposed for M-PSK (Phase Shift Keying). The ring codes have natural linear distance property for PSK. Therefore, the best code can be able to easily search. However, the ring codes do not have the property for QAM (Quadrature Amplitude Modulation). So in this paper, we propose suitable nonbinary convolutional codes for QAM. First, we introduce a method with a matched mapping to easily search the best code. Next, we search rate 1/2 nonbinary convolutional codes for 64-QAM with this method. In addition, new punctured convolutional codes are constructed from new convolutional codes and applied to 64-QAM coded modulation. Finally, we examine the bit error rate performance of 64-QAM coded modulation system using these new codes by computer simulations. The result shows the proposed coded modulation is effective for additive white Gaussian noise channels.