Multi-Edge Type LDPC codes
- 1. Multi-edge Type LDPC as step to achieve finite-length capacity 2013
- 3. We cook MET* *Multi-edge Type LDPC codes to achieve capacity, make better solutions and earn competition market…
- 4. Core idea to optimization process of threshold by Density Evolution instead of degree distribution use defined structures of protograph. For DE approximation instead Gaussian Approximation use RCA reciprocal-channel approximation (S.-Y. Chung) or protograph EXIT-chart (Gianluigi Liva). T. J. Richardson and R. L. Urbanke, “Multi-edge type LDPC codes,” in Workshop honoring Prof. Bob McEliece on his 60th birthday, California Institute of Technology, Pasadena, California, 2002.
- 5. Multi-edge approach based on the well know* idea of using puncturing under code on the graph with special distribution of erasure recovery *Turbo code (LTE) puncture some number of bit (around 7%) to improve error-correcting properties. Regular LDPC use punctured bits (precoding) to improve threshold. Staircase codes use punture in RS and etc….
- 6. Another important properties that MET-LDPC codes change influence of trapping set (TS) obtained by punctured nodes. Depend from structures of protograph it have some kind of cycles cancelation properties (like sequential cycles broking successive cancelation in Polar codes, but here same based on parallel scheduler ). Which simplify code design from one hand for linear size TS. From another hand make sublinear size TS analysis hard for cases of most threshold optimized multi cascade MET-LDPC protographs. Lowering error-floor for some moderate length codes using analytical tool (Ts weighed and protograph lifting) became where challenge problem.
- 7. We can puncture every second bit in RA and under BP layered scheduler it fast recover(Janis Dingel JASS05) We can not send some bit and make several cascade code which greatly improve threshold(ARJA and etc protographs, Reported Thresholds… Sarah J. Johnson)
- 8. Thorpe protograph J. Thorpe Low-Density Parity-Check (LDPC) Codes Constructed from Protographs IPN Progress Report 42-154
- 9. Divsalar’s AR4JA family of codes (R=0.8)
- 10. Cuizhu Shi; Ramamoorthy, A., "Design and analysis of E^2RC codes," in Selected Areas in Communications, IEEE Journal on , vol.27, no.6, pp.889-898
- 11. *Richardson T., R. Urbanke Multi-Edge Type LDPC Codes EBNo 0.409 DE Threshold Shannon 0.187 10001010101100000 01110111010110000 10111100110011000 00001011100001100 01010101011000100 01000000000000010 10100000000000001
- 12. Richardson Flarion Technologies, Inc. white paper “Vector-LDPC™ Codes for Mobile Broadband Communications”
- 13. Conclusions Within next 10 years MET-LDPC make quiet revolution in channel coding (and this general approach in ML, methods under factor graph). We’ll see how MET binary and non-binary LDPC codes occupied most of ECC solutions.
- 14. Cook MET or go away from market…