Spatially Coupled Turbo-Like Codes: A New Trade-Off Between Waterfall and Error Floor

Abstract

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.