Präfixcode

Präfixcode is a type of code where no codeword is a prefix of any other codeword. This property is crucial for unambiguous decoding of data streams. In practical terms, when a sequence of codewords is transmitted, the receiver can immediately identify the end of one codeword and the beginning of the next without needing any special delimiter symbols. This is because as soon as a received sequence matches a known codeword, it must be that codeword, as no longer codeword can begin with it.

The concept of prefix codes is fundamental in areas like data compression and information theory. For example, Huffman coding, a widely used compression algorithm, generates prefix codes. The structure of prefix codes allows for efficient decoding algorithms. Without the prefix property, disambiguation would require more complex mechanisms, potentially increasing processing time and data overhead.

A simple example of a prefix code is the set of binary codewords {0, 10, 11}. Here, '0' is not a prefix of '10' or '11'. Similarly, '10' is not a prefix of '11', and '11' is not a prefix of '10'. If we received the sequence '01011', we could uniquely decode it as '0', '10', '11'. If '10' were a prefix of '101', then '1010' could be decoded as '10' followed by '1', or as '101' followed by '0', leading to ambiguity. This highlights the importance of the prefix property for deterministic decoding.