kiholee/TOIFAS
1
0
Fork 0
Code Issues Pull Requests Actions Packages Projects Releases Wiki Activity

Structured key family as the main configuration

Browse Source 
Unconstrained key training converged to disjoint sparse supports: 99
percent of each users key energy sat on three or four of the sixteen
entries, with pairwise disjoint supports and one numerically dead
codebook column. That is an orthogonal slot allocation, so the
superposition collapsed into OMA and the key space was far smaller than
the dense direction the brute-force study assumes.

The main configuration is now the structured Walsh-Hadamard family,
which is dense, exactly orthogonal, unit modulus, and already the best
family in the key-family table. base_keys generalizes to any key length
by truncating the next power-of-two Sylvester order, and the key-length
sweep keeps only lengths where the truncated rows stay exactly
orthogonal, verified numerically.

Also fixes the M-PAM energy normalization in oma_ser_keylen, which used
sqrt(6g/(M^2-1)) where unit average symbol energy gives A^2=3/(M^2-1);
the closed form was 3 dB optimistic and now reproduces a direct Monte
Carlo to 1e-5.

Results move accordingly: the proposal now stays below OMA at every SNR
and reaches 1.52x at key length 64, while the jamming margin falls to
5.5-6.3 dB and the brute-force curve to 0.59 at a million guesses.
This commit is contained in:
KiHoLee
2026-08-17 20:02:27 +09:00
parent b120364e38
commit 3d5a7fc6f3
27 changed files with 561 additions and 418 deletions
Download Patch File Download Diff File Expand all files Collapse all files
data/sec_snr.csv
+11 -11
View File
@@ -1,12 +1,12 @@
snr_db,legit,eve_wrong,eve_none,eve_public,oma,chance
0,0.8944596875,0.9999621875,0.999988125,0.8945528125,0.8933480658,0.9999847412
2,0.79877875,0.9999559375,0.999986875,0.798940625,0.7973276257,0.9999847412
4,0.6697890625,0.9999446875,0.99998625,0.6702265625,0.6686275787,0.9999847412
6,0.5269903125,0.999944375,0.99999125,0.5272609375,0.525415822,0.9999847412
8,0.39087,0.9999415625,0.999988125,0.39062875,0.3892153151,0.9999847412
10,0.2760796875,0.9999296875,0.999986875,0.2753090625,0.2747696909,0.9999847412
12,0.1876809375,0.9999203125,0.9999884375,0.1878209375,0.1870712987,0.9999847412
14,0.1250471875,0.999920625,0.9999896875,0.12470875,0.1241256148,0.9999847412
16,0.0812634375,0.9999153125,0.999985625,0.08121,0.08092517452,0.9999847412
18,0.05243375,0.9999090625,0.9999865625,0.0526228125,0.05214810026,0.9999847412
20,0.0335228125,0.9999196875,0.999988125,0.033636875,0.03334949917,0.9999847412
0,0.8821684375,0.999989375,0.9999803125,0.8819953125,0.8933480658,0.9999847412
2,0.779363125,0.99999125,0.999980625,0.7794809375,0.7973276257,0.9999847412
4,0.6455015625,0.9999884375,0.9999809375,0.64627375,0.6686275787,0.9999847412
6,0.5016365625,0.9999903125,0.99998,0.5016371875,0.525415822,0.9999847412
8,0.3675334375,0.999989375,0.9999775,0.3677109375,0.3892153151,0.9999847412
10,0.2576425,0.99999375,0.999970625,0.2569871875,0.2747696909,0.9999847412
12,0.1741078125,0.99999,0.9999703125,0.17413125,0.1870712987,0.9999847412
14,0.115345,0.9999853125,0.999966875,0.1151475,0.1241256148,0.9999847412
16,0.0748184375,0.9999846875,0.9999675,0.0747059375,0.08092517452,0.9999847412
18,0.0480371875,0.9999884375,0.9999575,0.0481878125,0.05214810026,0.9999847412
20,0.030745,0.99998875,0.9999559375,0.0308409375,0.03334949917,0.9999847412
1 snr_db legit eve_wrong eve_none eve_public oma chance
2 0 0.8944596875 0.8821684375 0.9999621875 0.999989375 0.999988125 0.9999803125 0.8945528125 0.8819953125 0.8933480658 0.9999847412
3 2 0.79877875 0.779363125 0.9999559375 0.99999125 0.999986875 0.999980625 0.798940625 0.7794809375 0.7973276257 0.9999847412
4 4 0.6697890625 0.6455015625 0.9999446875 0.9999884375 0.99998625 0.9999809375 0.6702265625 0.64627375 0.6686275787 0.9999847412
5 6 0.5269903125 0.5016365625 0.999944375 0.9999903125 0.99999125 0.99998 0.5272609375 0.5016371875 0.525415822 0.9999847412
6 8 0.39087 0.3675334375 0.9999415625 0.999989375 0.999988125 0.9999775 0.39062875 0.3677109375 0.3892153151 0.9999847412
7 10 0.2760796875 0.2576425 0.9999296875 0.99999375 0.999986875 0.999970625 0.2753090625 0.2569871875 0.2747696909 0.9999847412
8 12 0.1876809375 0.1741078125 0.9999203125 0.99999 0.9999884375 0.9999703125 0.1878209375 0.17413125 0.1870712987 0.9999847412
9 14 0.1250471875 0.115345 0.999920625 0.9999853125 0.9999896875 0.999966875 0.12470875 0.1151475 0.1241256148 0.9999847412
10 16 0.0812634375 0.0748184375 0.9999153125 0.9999846875 0.999985625 0.9999675 0.08121 0.0747059375 0.08092517452 0.9999847412
11 18 0.05243375 0.0480371875 0.9999090625 0.9999884375 0.9999865625 0.9999575 0.0526228125 0.0481878125 0.05214810026 0.9999847412
12 20 0.0335228125 0.030745 0.9999196875 0.99998875 0.999988125 0.9999559375 0.033636875 0.0308409375 0.03334949917 0.9999847412