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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.
Compute forward probabilities ; Compute backward probabilities ; Compute smoothed probabilities based on other information (i.e. noise variance for AWGN, bit crossover probability for binary symmetric channel)
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.
Here, the variable c is first written to in S1 and then variable c is written to again in statement S2. This output dependence can be represented by S1 →O S2. An output dependence can be seen by different iterations in a loop. The following code snippet shows an example of this case:
Hardware-wise, this turbo code encoder consists of two identical RSC coders, C 1 and C 2, as depicted in the figure, which are connected to each other using a concatenation scheme, called parallel concatenation: In the figure, M is a memory register. The delay line and interleaver force input bits d k to appear in different sequences.
Numba is used from Python, as a tool (enabled by adding a decorator to relevant Python code), a JIT compiler that translates a subset of Python and NumPy code into fast machine code. Pythran compiles a subset of Python 3 to C++ . [165] RPython can be compiled to C, and is used to build the PyPy interpreter of Python.
Forward checking only checks whether each of the unassigned variables x 3 and x 4 is consistent with the partial assignment, removing the value 2 from their domains. The simpler technique for evaluating the effect of a specific assignment to a variable is called forward checking . [ 1 ]
The general algorithm involves message passing and is substantially similar to the belief propagation algorithm (which is the generalization of the forward-backward algorithm). With an algorithm called iterative Viterbi decoding , one can find the subsequence of an observation that matches best (on average) to a given hidden Markov model.