EXIT-Chart of SC-LDPC Spatial Coupling & Tail-biting Further Investigation Simulation results Block-LDPC SC-LDPC 1 1 0.9 0.9 0.8 0.8 0.7 0.7 I E,VND , I A,CND 0.6 I E,VND , I A,CND 0.6 0.5 0.5 0.4 0.4 0.3 0.3 0.2 0.2 I E,VND − variable nodes I E,VND − variable nodes 0.1 I E,CND − check nodes 0.1 I E,CND − check nodes trajectory trajectory 0 0 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 I A,VND , I E,CND I A,VND , I E,CND - tunnel-effect ( "micro-convergence" ) for SC-LDPC [ 1 ] [ 1 ] Schmalen, ten Brink, "Combining Spatially Coupled LDPC Codes with Modulation and Detection", SCC 2013, Munich, Germany 1/5
EXIT-Chart of SC-LDPC Spatial Coupling & Tail-biting Further Investigation Simulation results Spatial Coupling [ 2 ] Tail-biting v · ( L + m S ) R Term = 1 − c ≤ 1 − c R Tail = 1 − c v = R D v = R D D L D -rate-loss -no rate-loss (ring structure!) -performance loss L ...replication factor m S ...number of memory elements [ 2 ] S. Kudekar, T. Richardson, R. Urbanke, "Spatially coupled ensembles universally achieve capacity under belief propagation", IEEE Transactions on Information Theory, 7761-7813, 2013 2/5
EXIT-Chart of SC-LDPC Spatial Coupling & Tail-biting Further Investigation Simulation results Introduce window B with fraction α of known bits Generalization of SC-LDPC codes → A way to investigate the ignition of the decoding wave Open Questions -In terms of B , how large should α be taken to result the threshold saturation ? -Instead of uniform distribution, what is the best distribution for freezing bits on window B ? 3/5
EXIT-Chart of SC-LDPC Spatial Coupling & Tail-biting Further Investigation Simulation results Density Evolution for SC-LDPC with Tail-biting Tail-biting SC-LDPC (3,6) ensemble with α = 0 . 8 , B = 1 4/5
EXIT-Chart of SC-LDPC Spatial Coupling & Tail-biting Further Investigation Simulation results Thank you! 5/5
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