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@@ -405,11 +405,76 @@ def E9_ceiling(d=512, snr=60.0, ntr=200):
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'blind_mc', 'blind_pred'], rows)
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# ------------------------------------------------------------------
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def E10_whpad(beta=0.311, d=768, dpad=1024, ntr=200):
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"""Zero-padded WH at d=768 (padded to 1024) vs dense Haar at 768.
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The embedding (768) is zero-padded to 1024, masked by H_1024 D_u,
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and the exact per-coordinate Wiener uses the true prior (signal
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variance 1/768 on the active support, zero on the padding, so the
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padded coordinates are discarded). Reference: Haar masks at the
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native d=768 with the standard aware demultiplexer. Same per-block
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energy E_b = 1 and the same noise PSD; the padded block occupies
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dpad channel uses, a bandwidth cost of dpad/d."""
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print(chr(10) + '=== E10: zero-padded WH (768->1024) vs native Haar 768 ===')
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snr_db = np.arange(0, 41, 5)
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sigs = torch.tensor(10 ** (-snr_db / 20.0), dtype=torch.float32,
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device=DEV)
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nb = len(snr_db)
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H = np.array([[1.0]])
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while H.shape[0] < dpad:
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H = np.block([[H, H], [H, -H]])
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Ht = torch.tensor(H / math.sqrt(dpad), dtype=torch.float32, device=DEV)
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g = 1.0 - beta**2
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res = {'haar': np.zeros(nb), 'whpad': np.zeros(nb)}
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for _ in range(ntr):
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e1, e2 = embed_pair(d, beta)
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# ---- native Haar at 768 ----
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M1, M2 = haar_g(d), haar_g(d)
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Q = M1.T @ M2
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n = cnoise_g(d)
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r = (M1 @ e1 + M2 @ e2).to(torch.complex64).unsqueeze(0) \
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+ sigs.view(-1, 1) * n.unsqueeze(0)
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t1 = (M1.T.to(torch.complex64) @ r.unsqueeze(-1)).squeeze(-1)
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g1 = aware_g(t1, Q, beta, 1.0, sigs**2)
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res['haar'] += abscos(g1, e1)
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# ---- zero-padded WH at 1024 ----
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z = torch.zeros(dpad - d, device=DEV)
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e1p = torch.cat([e1, z]); e2p = torch.cat([e2, z])
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D1 = torch.tensor(np.sign(rng.standard_normal(dpad)),
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dtype=torch.float32, device=DEV)
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D2 = torch.tensor(np.sign(rng.standard_normal(dpad)),
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dtype=torch.float32, device=DEV)
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W1, W2 = Ht * D1.unsqueeze(0), Ht * D2.unsqueeze(0)
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npad = cnoise_g(dpad)
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rp = (W1 @ e1p + W2 @ e2p).to(torch.complex64).unsqueeze(0) \
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+ sigs.view(-1, 1) * npad.unsqueeze(0)
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tw = (W1.T.to(torch.complex64) @ rp.unsqueeze(-1)).squeeze(-1)
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q = (D1 * D2)[:d] # active coordinates only
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a = 1.0 + beta * q # (d,)
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s_var = 1.0 / d # true signal variance
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v = g / d + (sigs**2).view(-1, 1) # interference + noise
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gains = (s_var * a.unsqueeze(0)) / (a.unsqueeze(0)**2 * s_var + v)
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w1 = gains.to(torch.complex64) * tw[:, :d]
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res['whpad'] += abscos(w1, e1)
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for k in res:
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res[k] /= ntr
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rows = [[s, res['haar'][i], res['whpad'][i]]
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for i, s in enumerate(snr_db)]
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write_csv('wh_padding', ['snr_db', 'haar768', 'whpad1024'], rows)
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dev = res['haar'] - res['whpad']
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print(f' cosine delta (haar - whpad): max {dev.max():.4f}, '
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f'at 20 dB {dev[list(snr_db).index(20)]:.4f}, '
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f'at 40 dB {dev[-1]:.4f}')
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print(f' bandwidth cost: {dpad}/{d} = {dpad/d:.3f}x uses '
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f'(per-use rate factor {d/dpad:.3f})')
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if __name__ == "__main__":
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todo = set(sys.argv[1:])
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ALL = {"E2": E2_sic, "E3": E3_unconditional, "E4": E4_csi,
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"E5": E5_maskfam, "E7c": E7_multiuser, "E8": E8_mismatch,
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"E9": E9_ceiling}
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"E9": E9_ceiling, "E10": E10_whpad}
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for name, fn in ALL.items():
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if not todo or name in todo:
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fn()
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KiHoLee