Construction of Symbol Transformations for Non-Binary Turbo Codes with Lowered Error Floor

Non-binary variants of Turbo and LDPC codes are known to provide significantly improved error correcting performance over their binary counterparts in particular for short frame sizes. One of the reasons is the possibility to directly map the code symbols to constellation symbols of higher order modulations. Moreover, being defined over higher-order Galois fields GF(q), Non-binary Turbo Codes offer high degrees of freedom in the code and interleaver design. In this work, first we analyse the interplay between component codes through the interleaver. Then, we propose a suitable design methodology for a GF(q) symbol transformation applied to the encoded frames by one of the component codes. By modifying the values of encoded symbols by one component code with respect to the other, the aim of such a transformation is to avoid reproducing error-prone sequences while taking into account the effect of the interleaver. Without added complexity to the encoding or to the decoding process, the transformations constructed through the proposed methodology significantly lower the error floor of non-binary turbo codes. Indeed, in a case study for two GF(16) codes, we show an improvement of up to 3 decades in the error floor.