Spatially Coupled Turbo Like Codes: A New Trade Off Between Waterfall and Error Floor
Spatially coupled turbo like codes (SC TCs) have been shown to have excellent decoding thresholds due to the threshold saturation effect. Furthermore, even for moderate block lengths, the simulation results demonstrate a very good bit error rate performance in the waterfall region. In this paper, we discuss the effect of spatial coupling on the performance of TCs in the finite block length regime. We investigate the effect of coupling on the error floor performance of SC TCs by establishing conditions under which the spatial coupling either preserves or improves the minimum distance of TCs. This allows us to investigate the error floor performance of SC TCs by performing a weight enumerator function analysis of the corresponding uncoupled ensembles. Our results demonstrate that the spatial coupling changes the design trade off between the waterfall and error floor performance. Instead of optimizing the belief propagation (BP) threshold of uncoupled TCs, which in turn leads to a higher error floor, we can take advantage of the threshold saturation property of the SC TCs. Choosing strong ensembles, characterized by good maximum a posteriori (MAP) thresholds and low error floors, the corresponding SC TCs are then able to simultaneously approach capacity and achieve very low error floor.
IEEE Transactions on Communications