Enumerate LDPC Codes extrinsic message degree (EMD) Spectrum for cycles analysis (indirect Trapping sets analysis with sublinear and linear sizes)

Papers:

K. Deka, A. Rajesh and P. K. Bora, "On the equivalence of the ACE and the EMD of a cycle for the ACE spectrum constrained LDPC codes," 2014 8th International Symposium on Turbo Codes and Iterative Information Processing (ISTC), Bremen, 2014, pp. 67-71.

Tao Tian, C. R. Jones, J. D. Villasenor and R. D. Wesel, "Selective avoidance of cycles in irregular LDPC code construction," in IEEE Transactions on Communications, vol. 52, no. 8, pp. 1242-1247, Aug. 2004.

Example of EMD Spectrum Estimation from paper Tao at al.

Parity-check Matrix with 9 columns, 3 rows and circulant size 1 (not quasi-cyclic codes) but we can rewrite it in QC for

1 0 1 0 1 0 0 0 1

0 1 1 0 1 1 1 0 0

0 0 0 1 0 1 0 0 0

0 0 0 1 1 0 1 1 0

0 1 1 1 0 1 0 0 1

1 1 0 0 0 0 1 1 1

became

9 6 1

0 -1 0 -1 0 -1 -1 -1 0

-1 0 0 -1 0 0 0 -1 -1

-1 -1 -1 0 -1 0 -1 -1 -1

-1 -1 -1 0 0 -1 0 0 -1

-1 0 0 0 -1 0 -1 -1 0

0 0 -1 -1 -1 -1 0 0 0

after enumerating cycles up to 8 using command

getEMDDistribution.exe -file 9_3.txt -out out.txt -upperGirth 8

result at out.txt

girth = 4 11 cycles

EMD Number

1 2

2 9

girth = 6 51 cycles

EMD Number

0 8

1 19

2 18

3 6

girth = 8 170 cycles

EMD Number

0 50

1 57

2 54

3 9