A Design of Non-Binary Turbo Codes over Finite Fields Based on Gaussian Approximation and Union Bounds

In this paper, we develop capacity-approaching non- binary turbo codes defined over high-order finite fields. Since the performance of turbo codes is characterized by the convergence behavior of iterative decoding and error floor in the high SNR region, we attempt to design the non-binary turbo codes based on the following two-stage optimization processes: In the first stage, we employ a Gaussian approximation method for non-binary turbo codes and analyze the convergence property of iterative decoding. After reducing the search space by the first stage, the best component convolutional codes are identified by examining the truncated union bound under the assumption of the uniform interleaver. Simulation results demonstrate that our non-binary turbo codes as designed above can outperform the conventional non-binary LDPC codes.