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In contrast, convolutional codes are typically decoded using soft-decision algorithms like the Viterbi, MAP or BCJR algorithms, which process (discretized) analog signals, and which allow for much higher error-correction performance than hard-decision decoding.
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.
Near-optimal erasure codes trade correction capabilities for computational complexity: practical algorithms can encode and decode with linear time complexity. Fountain codes (also known as rateless erasure codes) are notable examples of near-optimal erasure codes.
In 2003, an irregular repeat accumulate (IRA) style LDPC code beat six turbo codes to become the error-correcting code in the new DVB-S2 standard for digital television. [13] The DVB-S2 selection committee made decoder complexity estimates for the turbo code proposals using a much less efficient serial decoder architecture rather than a ...
There are many different instances of turbo codes, using different component encoders, input/output ratios, interleavers, and puncturing patterns.This example encoder implementation describes a classic turbo encoder, and demonstrates the general design of parallel turbo codes.
A Reed–Solomon code (like any MDS code) is able to correct twice as many erasures as errors, and any combination of errors and erasures can be corrected as long as the relation 2E + S ≤ n − k is satisfied, where is the number of errors and is the number of erasures in the block.
It could happen that the Euclidean algorithm finds () of degree higher than () having number of different roots equal to its degree, where the Fourney formula would be able to correct errors in all its roots, anyway correcting such many errors could be risky (especially with no other restrictions on received word).
The algorithm is named after its inventors: Bahl, Cocke, Jelinek and Raviv. [1] This algorithm is critical to modern iteratively-decoded error-correcting codes, including turbo codes and low-density parity-check codes.