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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] This design has a better performance than any previously conceived concatenated codes.
This paper analyzed repeat-accumulate (RA) codes which are the serial concatenation of an inner two-state recursive convolutional code (also called an 'accumulator' or parity-check code) with a simple repeat code as the outer code, with both codes linked by an interleaver.
Low-density parity-check (LDPC) codes are a class of highly efficient linear block codes made from many single parity check (SPC) codes. They can provide performance very close to the channel capacity (the theoretical maximum) using an iterated soft-decision decoding approach, at linear time complexity in terms of their block length.
The Justesen code is the concatenation of an (,,) outer code and different (,,) inner codes , for.. More precisely, the concatenation of these codes, denoted by (,...,), is defined as follows.
The code construction is based on a multiple recursive concatenation of a short kernel code which transforms the physical channel into virtual outer channels. When the number of recursions becomes large, the virtual channels tend to either have high reliability or low reliability (in other words, they polarize or become sparse), and the data ...
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 ()).
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The distance d was usually understood to limit the error-correction capability to ⌊(d−1) / 2⌋. The Reed–Solomon code achieves this bound with equality, and can thus correct up to ⌊(n−k) / 2⌋ errors. However, this error-correction bound is not exact.