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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 ...
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 ...
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.
Kraft's inequality in some cases provides a quick way to exclude the possibility that a given code is uniquely decodable. Prefix codes and block codes are important classes of codes which are uniquely decodable by definition. Timeline of information theory; Post's correspondence problem is similar, yet undecidable.
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".
Algorithms developed for list decoding of several interesting code families have found interesting applications in computational complexity and the field of cryptography. Following is a sample list of applications outside of coding theory: Construction of hard-core predicates from one-way permutations. Predicting witnesses for NP-search problems.
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.
A locally decodable code is a code that allows a single bit of the original message to be recovered with high probability by only looking at a small portion of the received word. A code is q {\displaystyle q} -query locally decodable if a message bit, x i {\displaystyle x_{i}} , can be recovered by checking q {\displaystyle q} bits of the ...