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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]
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 ...
For example, an overall code rate of 1/2 may be achieved by puncturing the outer convolutional code to rate 3/4 and the inner convolutional code to rate 2/3. A recursive inner convolutional code is preferable for turbo decoding of the SCCC. The inner code may be punctured to a rate as high as 1/1 with reasonable performance.
Systems using LDPC codes therefore typically employ additional interleaving across the symbols within a code word. [23] For turbo codes, an interleaver is an integral component and its proper design is crucial for good performance.
To convolutionally encode data, start with k memory registers, each holding one input bit.Unless otherwise specified, all memory registers start with a value of 0. The encoder has n modulo-2 adders (a modulo 2 adder can be implemented with a single Boolean XOR gate, where the logic is: 0+0 = 0, 0+1 = 1, 1+0 = 1, 1+1 = 0), and n generator polynomials — one for each adder (see figure below).
In digital communications, a turbo equalizer is a type of receiver used to receive a message corrupted by a communication channel with intersymbol interference (ISI). It approaches the performance of a maximum a posteriori (MAP) receiver via iterative message passing between a soft-in soft-out (SISO) equalizer and a SISO decoder. [1]
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.
Interleaving can provide us with a (,) code that can correct all bursts of length , for any given . If we want to encode a message of an arbitrary length using interleaving, first we divide it into blocks of length λ k {\displaystyle \lambda k} .