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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.
The main idea is that if the inner block length is selected to be logarithmic in the size of the outer code then the decoding algorithm for the inner code may run in exponential time of the inner block length, and we can thus use an exponential-time but optimal maximum likelihood decoder (MLD) for the inner code.
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)
Turbo codes were so revolutionary at the time of their introduction that many experts in the field of coding did not believe the reported results. When the performance was confirmed a small revolution in the world of coding took place that led to the investigation of many other types of iterative signal processing.
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. The Global Positioning System makes corrections for receiver clock errors and other effects but there are still residual errors which are not corrected.
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.
Error-correcting codes are used in lower-layer communication such as cellular network, high-speed fiber-optic communication and Wi-Fi, [11] [12] as well as for reliable storage in media such as flash memory, hard disk and RAM. [13] Error-correcting codes are usually distinguished between convolutional codes and block codes:
Redundancy is used, here, to increase the chance of recovering from channel errors. This is a (6, 3) linear code , with n = 6 and k = 3. Again ignoring lines going out of the picture, the parity-check matrix representing this graph fragment is