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.
Resource-match the OMA reference in the key-length sweep (oma_ser_keylen),
which gives it the L/16 combining gain the longer frame allows. The
proposal now passes a resource-matched OMA by 1.27x at L=64 rather than
the 4.3x reported against a fixed-d reference.
Densify the JSR, sensitivity, and brute-force grids so the curves are
smooth, give the index cipher its channel floor instead of error-free
reception, and add the permutation-key known-plaintext attack
(exp_permkpa) so Fig. 7 carries a conventional linear scheme.
Add check_cov_attack.py and check_cov_ceiling.py: a referee raised a
ciphertext-only second-order attack; the exact-population test shows the
received covariance leaks only a sparse rank-deficient subset of the key
Gram and leaves the eavesdropper at the random-guess level.
Dump verify_math.csv, move the superseded V=256 pilot CSVs to data/pilot.
- exclude the all-ones Walsh-Hadamard row and test every key family
against the all-ones guess
- pass the model dimension to the noise scaling so the key-length sweep
runs at a fixed per-dimension SNR
- known-plaintext attack with nested accumulation and common random
numbers, averaged over 40 collections
- key sensitivity and brute-force search extended to the permutation
key and the index cipher
- make_tables regenerates all three result tables from the CSVs
KiHoLee