This document discusses multi-edge type (MET) low-density parity-check (LDPC) codes. MET-LDPC codes use defined protograph structures and density evolution to optimize thresholds and achieve capacity. Puncturing nodes in the protograph changes the influence of trapping sets and can provide cycle-canceling properties to simplify code design and lower error floors. Several examples of MET-LDPC protographs that improve thresholds through puncturing and cascading techniques are presented. The document predicts that MET-LDPC codes will revolutionize channel coding in the next 10 years and become a dominant error correction solution.

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
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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…