Description
Multiply positive averageSymbols by log2(alphabet) for bitsPerCodeword.
A code's symbol cost, length, overhead, and expected rate use different denominators. An ideal information budget is not necessarily the measured size of a practical encoded message.
Multiply positive averageSymbols by log2(alphabet) for bitsPerCodeword.
When to use this tool
Use Coding Efficiency Fixed Alphabet Term when you need one explicit coding-cost or redundancy component.
How to use the tool and how it works
- Enter entropyBits, averageSymbols, alphabet. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read bitsPerCodeword, efficiency. Use the output convention below.
Multiply positive averageSymbols by log2(alphabet) for bitsPerCodeword. Require nonnegative entropyBits no greater than that cost and divide entropy by cost for efficiency.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| entropyBits | Information entropy in bits on the same per-symbol basis as the code cost. | Required. Finite number; minimum 0. |
| averageSymbols | Average Symbols | Required. Finite number; strictly above 0. |
| alphabet | Alphabet | Required. Safe integer; minimum 2. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| bitsPerCodeword | Bits Per Codeword | Required. Finite number. |
| efficiency | Efficiency | Required. Finite number. |
{
"input": {
"entropyBits": 3,
"averageSymbols": 2,
"alphabet": 4
},
"output": {
"bitsPerCodeword": 4,
"efficiency": 0.75
}
}Limitations and assumptions
- Alphabet size is at least two; averageSymbols is a per-codeword average, and codebook feasibility and measured compression are not checked.
- 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
Inspect the complete codebook and format, including headers, termination, padding, and source probabilities.
References
Similar or alternative tools
- Information: Code Redundancy Per Symbol
Return their difference and 1 - entropy/averageCodeLength, or relativeRedundancy zero at a zero average.
- Entropy Rate Fixed Block Overhead
Multiply symbols by entropyPerSymbol for payloadBits, add headerBits, and divide by positive symbols for bitsPerSymbol.