{
  "title": "Illustrative optical on-off-keying link",
  "evidence": "Gaussian analytical model and seeded Monte Carlo; no hardware measurements",
  "parameters": {
    "seed": 690301,
    "bits_per_case": 200000,
    "wavelength_nm": 1550,
    "bitrate_bps": 1000000000.0,
    "noise_bandwidth_hz": 700000000.0,
    "transmitted_one_level_dbm": 0,
    "fixed_loss_db": 3,
    "attenuation_db_km": 0.2,
    "extinction_ratio": 10,
    "responsivity_a_w": 0.8,
    "dark_current_a": 1e-08,
    "load_ohm": 50,
    "electron_charge_c": 1.602176634e-19,
    "boltzmann_j_k": 1.380649e-23,
    "bit_one_probability": 0.5
  },
  "temperatures_k": [
    273.15,
    298.15,
    333.15
  ],
  "curve_rows": 903,
  "monte_carlo_rows": 18,
  "equations": {
    "loss_db": "3 + 0.20*d_km",
    "p1_w": "1e-3 * 10^(-loss_db/10)",
    "p0_w": "p1_w/10",
    "photocurrent": "0.8 * optical_power_w",
    "variance": "2*q*(I+Idark)*B + 4*k*T*B/R",
    "threshold": "(I1+I0)/2",
    "ber": "0.5*[Q((I1-threshold)/sigma1)+Q((threshold-I0)/sigma0)]",
    "Q": "0.5*erfc(x/sqrt(2))",
    "zero_count_upper95": "1-0.05^(1/N)"
  },
  "limitations": [
    "Transmitted and received power values refer to logical-one levels, not average optical power.",
    "Midpoint threshold and equally likely independent bits; unequal variances mean threshold is not asserted optimal.",
    "The constant dark-current mean is removed; dark current contributes shot noise.",
    "1550 nm identifies an illustrative band; wavelength is not a varied model input.",
    "Temperature affects only Johnson noise.",
    "No dispersion, clock recovery, wavelength multiplexing, laser intensity noise, nonlinearities, error correction or protocol.",
    "All hardware values and attenuation are scenario inputs, not measured specifications or a cable guarantee.",
    "Zero sampled errors is not zero error probability. One-sided bounds shown only for zero-count cases.",
    "Very small analytical tails can numerically underflow to zero; the plot omits such points rather than claiming perfect transmission."
  ],
  "checks": {
    "all_18_monte_carlo_within_declared_tolerance": true,
    "distance_monotonic": true
  },
  "parity_samples": [
    {
      "distance_km": 75,
      "temperature_k": 298.15,
      "received_one_level_dbm": -18.0,
      "one_power_w": 1.5848931924611134e-05,
      "zero_power_w": 1.5848931924611134e-06,
      "one_current_a": 1.2679145539688908e-05,
      "zero_current_a": 1.2679145539688908e-06,
      "one_sigma_a": 4.830785805482127e-07,
      "zero_sigma_a": 4.804220248004939e-07,
      "threshold_a": 6.973530046828899e-06,
      "analytic_ber": 1.2498299342356686e-32
    },
    {
      "distance_km": 100,
      "temperature_k": 298.15,
      "received_one_level_dbm": -23.0,
      "one_power_w": 5.011872336272725e-06,
      "zero_power_w": 5.011872336272725e-07,
      "one_current_a": 4.00949786901818e-06,
      "zero_current_a": 4.00949786901818e-07,
      "one_sigma_a": 4.810616093758278e-07,
      "zero_sigma_a": 4.802195931201527e-07,
      "threshold_a": 2.205223827959999e-06,
      "analytic_ber": 8.706018363927636e-05
    },
    {
      "distance_km": 125,
      "temperature_k": 333.15,
      "received_one_level_dbm": -28.0,
      "one_power_w": 1.584893192461114e-06,
      "zero_power_w": 1.584893192461114e-07,
      "one_current_a": 1.2679145539688913e-06,
      "zero_current_a": 1.2679145539688914e-07,
      "one_sigma_a": 5.078051223780699e-07,
      "zero_sigma_a": 5.075530346735202e-07,
      "threshold_a": 6.973530046828902e-07,
      "analytic_ber": 0.13053564600250778
    }
  ],
  "sources": [
    "https://www.itu.int/rec/T-REC-G.652-202408-I/en"
  ]
}