Description
Multiply nonnegative inputEntropyBits by erasureProbability for lostBits and subtract from input entropy for retainedBits.
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.
Multiply nonnegative inputEntropyBits by erasureProbability for lostBits and subtract from input entropy for retainedBits.
When to use this tool
Use Channel Erasure Information Loss Term when you need one supplied ideal-channel component.
How to use the tool and how it works
- Enter erasureProbability, inputEntropyBits. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read lostBits, retainedBits. Use the output convention below.
Multiply nonnegative inputEntropyBits by erasureProbability for lostBits and subtract from input entropy for retainedBits.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| erasureProbability | Erasure Probability | Required. Finite number; minimum 0; maximum 1. |
| inputEntropyBits | Input Entropy Bits | Required. Finite number; minimum 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| lostBits | Lost Bits | Required. Finite number. |
| retainedBits | Retained Bits | Required. Finite number. |
{
"input": {
"erasureProbability": 0.25,
"inputEntropyBits": 2
},
"output": {
"lostBits": 0.5,
"retainedBits": 1.5
}
}Limitations and assumptions
- This assumes independent erasure and error-free retained observations; actual channel behavior and entropy are supplied.
- 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 Channel Erasure Contribution
Compute binary entropy in bits from inputOneProbability, using zero at deterministic endpoints.
- Channel Erasure Output Mass Term
Split inputMass into inputMass × (1 - erasureProbability) retained and inputMass × erasureProbability erased.