The jammed OMA model now matches the transmit chain the paper
describes, the key-length sweep averages the eavesdropper over eight
substitute-key draws, and verify_math gains the coded-OMA outage
reference, symbolic checks of the three algebraic identities, and the
cross-period remainder of Proposition 2. The README records the energy
and channel conventions.
diag_maskdegen writes data/maskdegen.csv so the claim it supports is
traceable; the legend guard inflates by the marker radius and refuses a
legend that leaves the canvas; one legend size on every figure.
Every OMA reference takes the L/16 combining gain so the comparison
stays resource matched, four hardcoded copies of the configuration are
replaced by MAIN_D or the main curve, and stage_J's K-by-L Gaussian
draw becomes its exact scalar Beta equivalent.
check_texhealth.py flags control characters and bare macro stubs left
by a shell heredoc, a class of corruption that LaTeX compiles without
complaint. It skips when main.tex is absent, as in this package.
fig_sec_snr now carries an inset with the OMA-to-proposed SER ratio,
since the 1 to 9 percent advantage is invisible across two decades of
log axis, and save() now guards inset overlap as it guards the legend.
check_consistency covers the L=8 crossover, the inset ratio span, the
stated secret sizes, and the Fig. 5 curve coincidence: 29 assertions.
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.
check_consistency.py asserts every headline number against its raw CSV,
so a stale quoted value fails loudly instead of surviving a revision. It
skips the manuscript-side assertions when main.tex is absent, which is
the case in this package.
The blind-versus-permutation agreement is 0.002, not 0.0015, and the
resource-matched OMA is undefined below L=16 rather than wherever 16/L
is not an integer.
KiHoLee