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Convolutional code with any code rate can be designed based on polynomial selection; [15] however, in practice, a puncturing procedure is often used to achieve the required code rate. Puncturing is a technique used to make a m / n rate code from a "basic" low-rate (e.g., 1/ n ) 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] This design has a better performance than any previously conceived concatenated codes.
The term algebraic coding theory denotes the sub-field of coding theory where the properties of codes are expressed in algebraic terms and then further researched. [citation needed] Algebraic coding theory is basically divided into two major types of codes: [citation needed] Linear block codes; Convolutional codes
A convolutional code that is terminated is also a 'block code' in that it encodes a block of input data, but the block size of a convolutional code is generally arbitrary, while block codes have a fixed size dictated by their algebraic characteristics. Types of termination for convolutional codes include "tail-biting" and "bit-flushing".
The first class of turbo code was the parallel concatenated convolutional code (PCCC). Since the introduction of the original parallel turbo codes in 1993, many other classes of turbo code have been discovered, including serial concatenated convolutional codes and repeat-accumulate codes. Iterative turbo decoding methods have also been applied ...
The commonly used rule of thumb of a truncation depth of five times the memory (constraint length K-1) of a convolutional code is accurate only for rate 1/2 codes. For an arbitrary rate, an accurate rule of thumb is 2.5(K - 1)/(1−r) where r is the code rate. [1]
The Reed–Solomon code, like the convolutional code, is a transparent code. This means that if the channel symbols have been inverted somewhere along the line, the decoders will still operate. The result will be the inversion of the original data.
Error-correcting codes are usually distinguished between convolutional codes and block codes: Convolutional codes are processed on a bit-by-bit basis. They are particularly suitable for implementation in hardware, and the Viterbi decoder allows optimal decoding. Block codes are processed on a block-by-block basis. Early examples of block codes ...