Description
Compute binary entropy in bits from inputOneProbability, using zero at deterministic endpoints.
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.
Compute binary entropy in bits from inputOneProbability, using zero at deterministic endpoints.
When to use this tool
Use Binary Channel Erasure Contribution when you need one supplied ideal-channel component.
How to use the tool and how it works
- Enter erasureProbability, inputOneProbability. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read conditionalEntropyBits, retainedEntropyBits. Use the output convention below.
Compute binary entropy in bits from inputOneProbability, using zero at deterministic endpoints. Multiply by erasureProbability for conditionalEntropyBits and by its complement for retainedEntropyBits.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| erasureProbability | Erasure Probability | Required. Finite number; minimum 0; maximum 1. |
| inputOneProbability | Input One Probability | Required. Finite number; minimum 0; maximum 1. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| conditionalEntropyBits | Conditional Entropy Bits | Required. Finite number. |
| retainedEntropyBits | Retained Entropy Bits | Required. Finite number. |
{
"input": {
"erasureProbability": 0.25,
"inputOneProbability": 0.5
},
"output": {
"conditionalEntropyBits": 0.25,
"retainedEntropyBits": 0.75
}
}Limitations and assumptions
- This is an ideal independent binary erasure channel model; it does not estimate a real channel or optimize an input distribution.
- 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
- Channel Erasure Information Loss Term
Multiply nonnegative inputEntropyBits by erasureProbability for lostBits and subtract from input entropy for retainedBits.
- Information: Binary Channel Crossover Symmetry
Return one minus crossoverProbability and the smaller of the original and complementary probabilities.