- tunnel-effect ( "micro-convergence" ) for SC-LDPC [ 1 ] [ - - PowerPoint PPT Presentation

1/5 EXIT-Chart of SC-LDPC Spatial Coupling & Tail-biting Further Investigation Simulation results

Block-LDPC SC-LDPC

0.2 0.4 0.6 0.8 1 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 IA,VND, IE,CND IE,VND, IA,CND IE,VND − variable nodes IE,CND − check nodes trajectory 0.2 0.4 0.6 0.8 1 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 IA,VND, IE,CND IE,VND, IA,CND IE,VND − variable nodes IE,CND − check nodes trajectory

• 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

2/5 EXIT-Chart of SC-LDPC Spatial Coupling & Tail-biting Further Investigation Simulation results

Spatial Coupling [2] Tail-biting

RTerm

D

= 1 − c

v · (L+mS) L

≤ 1 − c

v = RD

RTail

D

= 1 − c

v = RD

• rate-loss
• no rate-loss (ring structure!)
• performance loss

L...replication factor mS...number of memory elements

[2] S. Kudekar, T. Richardson, R. Urbanke, "Spatially coupled ensembles universally achieve capacity under belief propagation", IEEE Transactions

• n Information Theory, 7761-7813, 2013

3/5 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?

4/5 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

5/5 EXIT-Chart of SC-LDPC Spatial Coupling & Tail-biting Further Investigation Simulation results

Thank you!