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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} .
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.
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]
There are different encoding procedures for the Reed–Solomon code, and thus, there are different ways to describe the set of all codewords. In the original view of Reed & Solomon (1960), every codeword of the Reed–Solomon code is a sequence of function values of a polynomial of degree less than .
Rate: 4/7 ~ 0.571: Distance: 3: Alphabet size: 2: ... all errors with a Hamming distance of 1 can be detected and corrected, which is the point of using a Hamming ...
Given a prime number q and prime power q m with positive integers m and d such that d ≤ q m − 1, a primitive narrow-sense BCH code over the finite field (or Galois field) GF(q) with code length n = q m − 1 and distance at least d is constructed by the following method.
As explained earlier, it can either detect and correct single-bit errors or it can detect (but not correct) both single and double-bit errors. With the addition of an overall parity bit, it becomes the [8,4] extended Hamming code and can both detect and correct single-bit errors and detect (but not correct) double-bit errors.
A special case of constant weight codes are the one-of-N codes, that encode bits in a code-word of bits.The one-of-two code uses the code words 01 and 10 to encode the bits '0' and '1'.