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Decodable text is a type of text often used in beginning reading instruction. Decodable texts are carefully sequenced to progressively incorporate words that are consistent with the letters and corresponding phonemes that have been taught to the new reader.
Locally testable codes have a lot in common with probabilistically checkable proofs (PCPs). This should be apparent from the similarities of their construction. In both, we are given random nonadaptive queries into a large string and if we want to accept, we must with probability 1, and if not, we must accept no more than half the time.
Locally decodable codes can also be concatenated, where a message is encoded first using one scheme, and the resulting codeword is encoded again using a different scheme. (Note that, in this context, concatenation is the term used by scholars to refer to what is usually called composition; see [5]). This might be useful if, for example, the ...
This is quite significant because it proves the existence of (,)-list-decodable codes of good rate with a list-decoding radius much larger than . In other words, the Johnson bound rules out the possibility of having a large number of codewords in a Hamming ball of radius slightly greater than d 2 {\displaystyle {\tfrac {d}{2}}} which means that ...
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 uniquely decodable codes that are not prefix codes; for instance, the reverse of a prefix code is still uniquely decodable (it is a suffix code), but it is not ...
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 ...
Let each source symbol from the alphabet = {,, …,} be encoded into a uniquely decodable code over an alphabet of size with codeword lengths ,, …,. Then = Conversely, for a given set of natural numbers ,, …, satisfying the above inequality, there exists a uniquely decodable code over an alphabet of size with those codeword lengths.
In coding theory, the Sardinas–Patterson algorithm is a classical algorithm for determining in polynomial time whether a given variable-length code is uniquely decodable, named after August Albert Sardinas and George W. Patterson, who published it in 1953. [1]
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