Capacity-Approaching Non-Binary Turbo Codes: A Hybrid Design Based on EXIT Charts and Union Bounds

Abstract

In this paper, we introduce a novel design approach for capacity-approaching non-binary turbo codes. There are two important factors that impact the performance of turbo codes in general: 1) the convergence behavior of iterative decoding in the low signal-to-noise ratio (SNR) and 2) the error-floor effect in the high SNR. We thus design the non-binary turbo codes by means of the EXIT charts and truncated union bounds. We first reduce the search space of component recursive convolutional codes by the analysis based on the truncated union bounds in conjunction with the uniform interleaver, followed by its optimization through the EXIT chart analysis. The construction of the EXIT chart for non-binary turbo codes with fixed code coefficients is a non-trivial task by the fact that these messages have multiple parameters to identify. Therefore, we develop a new EXIT chart analysis for non-binary messages which does not rely on any specific message model. It is demonstrated through computer simulations that the well-designed non-binary turbo codes achieve a better performance than their binary counterparts as well as the conventional non-binary LDPC codes of the same field size. Furthermore, the code design is extended to high-order modulation, and our turbo codes designed for quadrature amplitude modulation are shown to outperform the conventional turbo trellis coded modulation schemes.