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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_jam_gap.csv
+200 -200
View File
@@ -1,201 +1,201 @@
ser,gap_db
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1 ser gap_db
2 0.7203966667 0.6026633333 7.395409349 5.493678481
3 0.7217858794 0.6046408543 7.394580398 5.495143167
4 0.7231750921 0.6066183752 7.393751447 5.496607853
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7 0.7273427303 0.612550938 7.391264594 5.50100191
8 0.728731943 0.614528459 7.390435644 5.502466596
9 0.7301211558 0.6165059799 7.389606693 5.503931281
10 0.7315103685 0.6184835008 7.388777742 5.505395967
11 0.7328995812 0.6204610218 7.387948791 5.506860653
12 0.734288794 0.6224385427 7.38711984 5.508301835
13 0.7356780067 0.6244160637 7.386290889 5.509221054
14 0.7370672194 0.6263935846 7.385461939 5.510140274
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16 0.7398456449 0.6303486265 7.383804037 5.511978713
17 0.7412348576 0.6323261474 7.382975086 5.512897932
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21 0.7467917085 0.6402362312 7.393359371 5.516574809
22 0.7481809213 0.6422137521 7.39657265 5.517494029
23 0.749570134 0.644191273 7.39978593 5.518413248
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25 0.7523485595 0.6481463149 7.406212489 5.520251687
26 0.7537377722 0.6501238358 7.409425768 5.521170906
27 0.7551269849 0.6521013568 7.412639048 5.522090126
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29 0.7579054104 0.6560563987 7.419065607 5.523928564
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31 0.7606838358 0.6600114405 7.425492166 5.525767003
32 0.7620730486 0.6619889615 7.428705445 5.526686223
33 0.7634622613 0.6639664824 7.431918725 5.527605442
34 0.764851474 0.6659440034 7.435132004 5.528524661
35 0.7662406868 0.6679215243 7.438345284 5.529443881
36 0.7676298995 0.6698990452 7.441558563 5.5303631
37 0.7690191122 0.6718765662 7.444771843 5.53128232
38 0.770408325 0.6738540871 7.447985122 5.532201539
39 0.7717975377 0.675831608 7.451198402 5.533120758
40 0.7731867504 0.677809129 7.454411681 5.534039978
41 0.7745759631 0.6797866499 7.457624961 5.534959197
42 0.7759651759 0.6817641709 7.46083824 5.535878416
43 0.7773543886 0.6837416918 7.46405152 5.535503786
44 0.7787436013 0.6857192127 7.467264799 5.533851599
45 0.7801328141 0.6876967337 7.470478079 5.532199412
46 0.7815220268 0.6896742546 7.473691358 5.530547225
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48 0.7843004523 0.6936292965 7.480117917 5.52724285
49 0.785689665 0.6956068174 7.483331197 5.525590663
50 0.7870788777 0.6975843384 7.486544476 5.523938475
51 0.7884680905 0.6995618593 7.489757756 5.522286288
52 0.7898573032 0.7015393802 7.492971035 5.522063588
53 0.7912465159 0.7035169012 7.493110679 5.525405405
54 0.7926357286 0.7054944221 7.4893604 5.528747221
55 0.7940249414 0.707471943 7.485610121 5.532089038
56 0.7954141541 0.709449464 7.481859841 5.535430855
57 0.7968033668 0.7114269849 7.478109562 5.538772672
58 0.7981925796 0.7134045059 7.474359282 5.542114488
59 0.7995817923 0.7153820268 7.470609003 5.545456305
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