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The description above is given for what is now called a serially concatenated code. Turbo codes, as described first in 1993, implemented a parallel concatenation of two convolutional codes, with an interleaver between the two codes and an iterative decoder that passes information forth and back between the codes. [6]
Turbo coding is an iterated soft-decoding scheme that combines two or more relatively simple convolutional codes and an interleaver to produce a block code that can perform to within a fraction of a decibel of the Shannon limit.
An error-correcting code is a way of encoding x as a message such that Bob will successfully understand the value x as intended by Alice, even if the message Alice sends and the message Bob receives differ. In an error-correcting code with feedback, the channel is two-way: Bob can send feedback to Alice about the message he received.
Lawson-Perfect's approach is to represent each part of a question as a function of the answer to the previous part. That is, if a student answer's "x" for part a, the correct answer to part b is "f(x)." No matter what the student puts for part a, the corresponding answer for part b can be calculated quickly.
All error-detection and correction schemes add some redundancy (i.e., some extra data) ... 1010 1010 1010 in the previous example would be detected as correct).
Consider the input code as 1101 1110 0001 0110 (this is the previous code with one error). We know the degree of the polynomial p x {\textstyle p_{x}} is at most r = 2 {\textstyle r=2} , we start by searching for monomial of degree 2.
Proof. We need to prove that if you add a burst of length to a codeword (i.e. to a polynomial that is divisible by ()), then the result is not going to be a codeword (i.e. the corresponding polynomial is not divisible by ()).
The first table, d, is based on multiplication in the dihedral group D 5. [7] and is simply the Cayley table of the group.Note that this group is not commutative, that is, for some values of j and k, d(j,k) ≠ d(k, j).