What is the definition of a variable-length code in information theory?

Conditions

• Applies to a single code mapping across all symbols in its alphabet.
• At least two codewords in the code have different bit lengths.

Reasoning, step by step

1. Identify the set of codewords assigned to the source symbols under a specific code.
2. Measure the bit length of each codeword.
3. Check if there is any variation in the lengths.
4. Conclude that the code is variable-length if at least one pair of codewords has different lengths.

Example

In the displayed example table, Codes 3, 4, 5, and 6 are marked as variable-length because different symbols receive binary strings of different sizes, such as 1-bit, 2-bit, or 4-bit words.

Common misconceptions

• Assuming that variable-length means every codeword must have a unique length.
• Confusing variable-length codes with prefix-free codes, which impose a structural constraint on the codewords.

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Explore next

• What is the definition of a fixed-length code?
• Which named coding methods are given as examples of variable-length coding?