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Say the code has codewords, then there are codewords that differ from a codeword by a burst of length . Each of the M {\displaystyle M} words must be distinct, otherwise the code would have distance < 1 {\displaystyle <1} .
If the number of errors within a code word exceeds the error-correcting code's capability, it fails to recover the original code word. Interleaving alleviates this problem by shuffling source symbols across several code words, thereby creating a more uniform distribution of errors. [ 21 ]
The rate of a code is inversely related to the query complexity, but the exact shape of this tradeoff is a major open problem. [8] [9] It is known that there are no LDCs that query the codeword in only one position, and that the optimal codeword size for query complexity 2 is exponential in the size of the original message. [8]
The rate of a block code is defined as the ratio between its message length and its block length: ... errors. Because a codeword is the only codeword in the ...
Once a polynomial is determined, then any errors in the codeword can be corrected, by recalculating the corresponding codeword values. Unfortunately, in all but the simplest of cases, there are too many subsets, so the algorithm is impractical. The number of subsets is the binomial coefficient, () =!
The complete block has m + n bits of data with a code rate of m/(m + n). The permutation of the payload data is carried out by a device called an interleaver . Hardware-wise, this turbo code encoder consists of two identical RSC coders, C 1 and C 2 , as depicted in the figure, which are connected to each other using a concatenation scheme ...
The code rate of the octet oriented Reed Solomon block code denoted RS(204,188) is 188/204, meaning that 204 − 188 = 16 redundant octets (or bytes) are added to each block of 188 octets of useful information.
Codes in general are often denoted by the letter C, and a code of length n and of rank k (i.e., having n code words in its basis and k rows in its generating matrix) is generally referred to as an (n, k) code. Linear block codes are frequently denoted as [n, k, d] codes, where d refers to the code's minimum Hamming distance between any two code ...