What is the definition of a uniquely decodable code?

Conditions

• Concerns decoding of concatenated codeword sequences at the receiver.
• The video does not state a formal symbolic definition beyond the examples and prose.

Reasoning, step by step

1. Consider a received binary sequence formed by concatenating codewords.
2. Attempt to segment the sequence into valid codewords from the code.
3. Verify that there is only one possible valid segmentation.
4. Conclude that the code is uniquely decodable.

Example

The video presents the code {0, 01, 011, 0111} as an example. Although it is not prefix-free, the sequence 0111 decodes uniquely as $x_4$, because alternative splits like $0+111$ or $01+11$ leave invalid residual bits.

Common misconceptions

• Assuming that all uniquely decodable codes must be prefix-free.
• Confusing unique decodability with instantaneous decoding, which is a stricter operational property.

Watch the explanation

Explore next

• Why does the video say prefix-freeness is sufficient but not necessary for unique decodability?
• What is the relationship between instantaneous codes and prefix-free codes in this lesson?