Description
Return one minus crossoverProbability and the smaller of the original and complementary probabilities.
Ideal binary crossover and erasure channels describe different forms of lost information. Their simple probability terms depend on assumptions about independence and error-free nonerased observations.
Return one minus crossoverProbability and the smaller of the original and complementary probabilities.
When to use this tool
Use Information: Binary Channel Crossover Symmetry when you need one supplied ideal-channel component.
How to use the tool and how it works
- Enter crossoverProbability. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read result. Expand result to inspect the returned fields.
Return one minus crossoverProbability and the smaller of the original and complementary probabilities. Mark outputRelabelingRequired only when crossoverProbability exceeds 0.5.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| crossoverProbability | Crossover Probability | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| result | Result | Required. Object. |
| result.complementaryCrossoverProbability | Complementary Crossover Probability | Calculated result member: number. |
| result.symmetryRepresentative | Symmetry Representative | Calculated result member: number. |
| result.outputRelabelingRequired | Output Relabeling Required | Calculated result member: boolean. |
{
"input": {
"crossoverProbability": 0.75
},
"output": {
"result": {
"complementaryCrossoverProbability": 0.25,
"symmetryRepresentative": 0.25,
"outputRelabelingRequired": true
}
}
}Limitations and assumptions
- This is the symmetry of an ideal binary crossover model under output relabeling, not an actual channel correction or capacity calculation.
- Outputs are nested inside result. Inputs must satisfy both the field types and the cross-field conditions above. Invalid input causes an error; a successful false flag or documented placeholder is a different result.
- Numeric calculations use binary floating point unless exact decimal-integer arithmetic is explicitly stated. No hidden measurement tolerance or decimal rounding is added; nonfinite or out-of-contract results are rejected. Numeric signed-zero results are exported as zero.
Alternative or Complementary methods
Estimate the actual channel and evaluate complete input/output distributions before predicting transmission performance.
References
Similar or alternative tools
- Binary Erasure Posterior Mass
When erased is true, return priorOne.
- Binary Channel Erasure Contribution
Compute binary entropy in bits from inputOneProbability, using zero at deterministic endpoints.