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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 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.
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)
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.
"Flexibility" here means that C need not refer to A or B in any way, as the switching of forwarding is abstracted from C. In this example, class C can forward to any class that implements an interface I. Class C has a method to switch to another forwarder. Including the implements clauses improves type safety, because each class must implement ...
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:
The analysis of errors computed using the global positioning system is important for understanding how GPS works, and for knowing what magnitude errors should be expected.
This process is implemented by Reed–Solomon codes, with code words constructed over a finite field using a Vandermonde matrix. Most practical erasure codes are systematic codes-- each one of the original k symbols can be found copied, unencoded, as one of the n message symbols. [12]