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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.
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.
Serial concatenated convolutional codes; Shaping codes; Slepian–Wolf coding; Snake-in-the-box; Soft-decision decoder; Soft-in soft-out decoder; Sparse graph code; Srivastava code; Stop-and-wait ARQ; Summation check
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.
Parity check is the special case where n = k + 1.From a set of k values {}, a checksum is computed and appended to the k source values: + = =. The set of k + 1 values {} + is now consistent with regard to the checksum.
LDPC codes have no limitations of minimum distance, [34] that indirectly means that LDPC codes may be more efficient on relatively large code rates (e.g. 3/4, 5/6, 7/8) than turbo codes. However, LDPC codes are not the complete replacement: turbo codes are the best solution at the lower code rates (e.g. 1/6, 1/3, 1/2). [35] [36]
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.