Entropy Rate Fixed Block Overhead Tool

Description

Multiply symbols by entropyPerSymbol for payloadBits, add headerBits, and divide by positive symbols for bitsPerSymbol.

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 symbols by entropyPerSymbol for payloadBits, add headerBits, and divide by positive symbols for bitsPerSymbol.

When to use this tool

Use Entropy Rate Fixed Block Overhead when you need one explicit coding-cost or redundancy component.

How to use the tool and how it works

Enter symbols, entropyPerSymbol, headerBits. Use the units and conventions below.
Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
Read payloadBits, totalBits, bitsPerSymbol. Use the output convention below.

Multiply symbols by entropyPerSymbol for payloadBits, add headerBits, and divide by positive symbols for bitsPerSymbol.^[1]

Input field	Meaning and units	Accepted input
symbols	Symbols	Required. Safe integer; minimum 1.
entropyPerSymbol	Supplied entropy in bits per source symbol.	Required. Finite number.
headerBits	Header Bits	Required. Safe integer; minimum 0.

Output field	Interpretation	Returned shape
payloadBits	Payload Bits	Required. Finite number.
totalBits	Total Bits	Required. Finite number.
bitsPerSymbol	Bits Per Symbol	Required. Finite number.

json

{
  "input": {
    "symbols": 8,
    "entropyPerSymbol": 2,
    "headerBits": 8
  },
  "output": {
    "payloadBits": 16,
    "totalBits": 24,
    "bitsPerSymbol": 3
  }
}

Limitations and assumptions

Entropy is supplied in bits per symbol; this idealized budget is not an achievable compressor size or an estimated entropy rate.
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

Calculation and input contract: information/entropy-rate-fixed-block-overhead — tool.io

Similar or alternative tools

Compression Ratio Header Excluded Base
Subtract header from positive stored size to obtain a positive payload, then divide original by payload for ratio.
Codebook Fixed Block Padding Cost
Compute (-symbols) modulo positive blockSize for paddingSymbols and multiply by bitsPerSymbol for paddingBits.