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Prefix code

As explained in Advanced Algorithms and Data Structures

A prefix code is a code in which no valid code sequence is a prefix of another valid code sequence.

A prefix code assigns valid sequences so that no sequence is the prefix of another. This makes compressed data immediately decodable: each complete sequence identifies one character without separators. section 2.8.3

Huffman coding constructs prefix codes with a binary tree:

  • Traverse left edges by adding 0 and right edges by adding 1 to the sequence. section 2.8.3
  • Use shorter sequences for more frequent characters, supporting efficient compression. section 2.8.3

Decoding 1001101

Following the tree, 10 decodes as B, 0 as A, and 1101 as D, producing “BAD”. The prefix property makes each boundary unambiguous. section 2.8.3

How Advanced Algorithms and Data Structures covers it

How deep it goes
Explains prefix freedom through tree traversal and demonstrates decoding, without developing a formal proof.
Examples
Uses the codes A=0, B=10, D=1101 and the compressed sequence 1001101 decoding to “BAD”.
What you can do after
Apply it via Huffman coding to construct character codes that can be decoded without explicit separators.
How it connects
Connects prefix codes with Huffman coding, binary trees, priority queues, and data compression.
Cover of Advanced Algorithms and Data Structures
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