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Consider the code {,,,,}.This code, which is based on an example by Berstel, [3] is an example of a code which is not uniquely decodable, since the string 011101110011. can be interpreted as the sequence of codewords
A code is uniquely decodable if its extension is § non-singular.Whether a given code is uniquely decodable can be decided with the Sardinas–Patterson algorithm.. The mapping = {,,} is uniquely decodable (this can be demonstrated by looking at the follow-set after each target bit string in the map, because each bitstring is terminated as soon as we see a 0 bit which cannot follow any ...
If Kraft's inequality holds with strict inequality, the code has some redundancy. If Kraft's inequality holds with equality, the code in question is a complete code. [2] If Kraft's inequality does not hold, the code is not uniquely decodable. For every uniquely decodable code, there exists a prefix code with the same length distribution.
For example, a code with code {9, 55} has the prefix property; a code consisting of {9, 5, 59, 55} does not, because "5" is a prefix of "59" and also of "55". A prefix code is a uniquely decodable code: given a complete and accurate sequence, a receiver can identify each word without requiring a special marker between words. However, there are ...
In computer science and information theory, a Huffman code is a particular type of optimal prefix code that is commonly used for lossless data compression.The process of finding or using such a code is Huffman coding, an algorithm developed by David A. Huffman while he was a Sc.D. student at MIT, and published in the 1952 paper "A Method for the Construction of Minimum-Redundancy Codes".
The Hadamard code is a locally decodable code, which provides a way to recover parts of the original message with high probability, while only looking at a small fraction of the received word. This gives rise to applications in computational complexity theory and particularly in the design of probabilistically checkable proofs .
The prefix code {00, 11} is not self-synchronizing; while 0, 1, 01 and 10 are not codes, 00 and 11 are. The prefix code {ab,ba} is not self-synchronizing because abab contains ba. The prefix code b ∗ a (using the Kleene star) is not self-synchronizing (even though any new code word simply starts after a) because code word ba contains code word a.
It has been shown that every code can be list decoded using small lists beyond half the minimum distance up to a bound called the Johnson radius. This is quite significant because it proves the existence of (,)-list-decodable codes of good rate with a list-decoding radius much larger than .