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.
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.
Give the orthogonal-access jammer its own Rayleigh channel in
oma_ser_jammed, matching the convention every simulated scheme already
used. Without it the closed-form curve faced a jammer at full power in
every frame while the Monte Carlo curves faced a fading one, which
inverted the ordering of the comparison.
Measure the outsider error rate for the fixed-key and naive-refresh
cases as well, and emit the two refresh tables from make_tables.py, so
no cell of the paper is hand-typed.
Derives each block key from the transformations that leave the decision
statistic invariant: a global sign per frame entry, a relabeling of the
frame entries applied to keys and codebook together, and a permutation
of which user holds which row. The legitimate error rate is unchanged
at 0.257 across 24 blocks while a refresh that installs fresh
orthogonal keys reaches 0.710, and a key recovered by known plaintext
returns to the random-guess level one block later.
KiHoLee