Description
Split inputMass into inputMass × (1 - erasureProbability) retained and inputMass × erasureProbability erased.
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.
Split inputMass into inputMass × (1 - erasureProbability) retained and inputMass × erasureProbability erased.
When to use this tool
Use Channel Erasure Output Mass Term when you need one supplied ideal-channel component.
How to use the tool and how it works
- Enter inputMass, erasureProbability. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read retainedMass, erasedMass. Use the output convention below.
Split inputMass into inputMass × (1 - erasureProbability) retained and inputMass × erasureProbability erased.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| inputMass | Input Mass | Required. Finite number; minimum 0; maximum 1. |
| erasureProbability | Erasure Probability | Required. Finite number; minimum 0; maximum 1. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| retainedMass | Retained Mass | Required. Finite number. |
| erasedMass | Erased Mass | Required. Finite number. |
{
"input": {
"inputMass": 0.5,
"erasureProbability": 0.25
},
"output": {
"retainedMass": 0.375,
"erasedMass": 0.125
}
}Limitations and assumptions
- Both inputs are fractions in [0, 1]; this is one channel mass term without a complete distribution or observed transmissions.
- 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.
- Binary Erasure Posterior Mass
When erased is true, return priorOne.