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Channel encoding of source of signals; Mechanical sub-processes of preparing a master disc, producing user discs and sensing the signals embedded on user discs while playing – the channel; Decoding the signals sensed from user discs; The process is subject to both burst errors and random errors. [7]
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 repeat and distribute operations perform the function of the interleaver in the turbo code. The ability to more precisely manage the connections of the various constituent codes and the level of redundancy for each input bit give more flexibility in the design of LDPC codes, which can lead to better performance than turbo codes in some ...
The on-line textbook: Information Theory, Inference, and Learning Algorithms, by David J.C. MacKay, contains chapters on elementary error-correcting codes; on the theoretical limits of error-correction; and on the latest state-of-the-art error-correcting codes, including low-density parity-check codes, turbo codes, and fountain codes.
Linearity guarantees that the minimum Hamming distance d between a codeword c 0 and any of the other codewords c ≠ c 0 is independent of c 0. This follows from the property that the difference c − c 0 of two codewords in C is also a codeword (i.e., an element of the subspace C), and the property that d(c, c 0) = d(c − c 0, 0). These ...
The distance of the concatenated code C out ∘C in is at least dD, that is, it is a [nN, kK, D'] code with D' ≥ dD. Proof: Consider two different messages m 1 ≠ m 2 ∈ B K. Let Δ denote the distance between two codewords. Then ((), ()).
In coding theory, the repetition code is one of the most basic linear error-correcting codes. In order to transmit a message over a noisy channel that may corrupt the transmission in a few places, the idea of the repetition code is to just repeat the message several times. The hope is that the channel corrupts only a minority of these repetitions.