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, simulation results demonstrate very good bit error rate performance (BER) 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 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 (WEF) analysis of the corresponding uncoupled ensembles. While uncoupled TC ensembles with close-to-capacity performance exhibit a high error floor, our results show that SC-TCs can simultaneously approach capacity and achieve very low error floor.Index Terms-Bound on minimum distance, expurgated bounds,spatially coupled turbo-like codes, union bound, weight enumerator analysis Parts of this paper have been presented at the IEEE International Symposium on Information Theory and Its Applications (ISITA), 2016.

Towards Fully Pipelined Decoding of Spatially Coupled Serially Concatenated Codes

“…SCCs can be described by a compact graph [11] as shown in Fig. 1(a), where the information and parity sequences are rep- The outer encoder receives the information sequence, u t , of length K bits and produces the K-bit outer parity sequence, p O t .…”

“…In the literature, most evaluations of the finite length performance have considered only coupling memory m = 1 [10], [11], although the asymptotic thresholds are slightly improved for larger m [7]. We have demonstrated in [12] how to use higher coupling memories without increasing the complexity and latency.…”

“…6(b) illustrates the performance of the proposed scheme and the uncoupled codes, SCCs, for different latencies. Also, the corresponding decoding thresholds, i.e., theoretical limit on the performance [11], are shown by vertical lines. It can be seen that in all cases the proposed scheme outperforms the SCCs by 0.2-0.8 dB.…”

Spatially Coupled Serially Concatenated Codes: Performance Evaluation and VLSI Design Tradeoffs

“…Recently, spatial coupling gives a new perspective of code design and improves the decoding threshold of turbo-like codes [2]. The main idea is to construct powerful long codes using small component codes.…”

“…As a result, the threshold of an iterative belief propagation (BP) decoder is improved to that of the optimal maximum-a-posteriori (MAP) decoder. This phenomenon is referred to as threshold saturation [2], which makes it possible to achieve Shannon limit by coupling the classical turbo-like codes, while without spatial coupling a significant gap exists between BP and MAP thresholds [2].…”