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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 β {\displaystyle \beta } Compute smoothed probabilities based on other information (i.e. noise variance for AWGN , bit crossover probability for binary symmetric channel )
The description above is given for what is now called a serially concatenated code. Turbo codes, as described first in 1993, implemented a parallel concatenation of two convolutional codes, with an interleaver between the two codes and an iterative decoder that passes information forth and back between the codes. [6]
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.
Specifically, the for loop will call a value's into_iter() method, which returns an iterator that in turn yields the elements to the loop. The for loop (or indeed, any method that consumes the iterator), proceeds until the next() method returns a None value (iterations yielding elements return a Some(T) value, where T is the element type).
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
The backward algorithm complements the forward algorithm by taking into account the future history if one wanted to improve the estimate for past times. This is referred to as smoothing and the forward/backward algorithm computes (|:) for < <. Thus, the full forward/backward algorithm takes into account all evidence.
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: