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In information theory , turbo codes originally in French Turbocodes are a class of high-performance forward error correction FEC codes developed around —91 but first published in , which were the first practical codes to closely approach the channel capacity , a theoretical maximum for the code rate at which reliable communication is still possible given a specific noise level. Turbo codes are nowadays competing with LDPC codes , which provide similar performance. The name "turbo code" arose from the feedback loop used during normal turbo code decoding, which was analogized to the exhaust feedback used for engine turbocharging.
Hagenauer has argued the term turbo code is a misnomer since there is no feedback involved in the encoding process. The fundamental patent application for turbo codes was filed on April 23, The patent application lists Claude Berrou as the sole inventor of turbo codes. The patent filing resulted in several patents including US Patent 5,, , which expired August 29, The paper was formed from three separate submissions that were combined due to space constraints. The merger caused the paper to list three authors: However, it is clear from the original patent filing that Claude Berrou is the sole inventor of turbo codes and that the other authors of the paper contributed material other than the core concepts of turbo codes.
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 first class of turbo code was the parallel concatenated convolutional code PCCC. Since the introduction of the original parallel turbo codes in , many other classes of turbo code have been discovered, including serial versions serial concatenated convolutional codes and repeat-accumulate codes.
Iterative turbo decoding methods have also been applied to more conventional FEC systems, including Reed-Solomon corrected convolutional codes, although these systems are too complex for practical implementations of iterative decoders. Turbo equalization also flowed from the concept of turbo coding. In addition to the invention of Turbo Codes, Claude Berrou also invented recursive systematic convolutional RSC codes, which are used in the example implementation of turbo codes described in the patent.
Prior to turbo codes, the best constructions were serial concatenated codes based on an outer Reed-Solomon error correction code combined with an inner Viterbi-decoded short constraint length convolutional code , also known as RSV codes. In a later paper, Berrou generously gave credit to the intuition of "G.
Hoeher, who, in the late 80s, highlighted the interest of probabilistic processing. Tanner had already imagined coding and decoding techniques whose general principles are closely related," although the necessary calculations were impractical at that time. This example encoder implementation describes a classic turbo encoder, and demonstrates the general design of parallel turbo codes. This encoder implementation sends three sub-blocks of bits. The first sub-block is the m -bit block of payload data.
Thus, two redundant but different sub-blocks of parity bits are sent with the payload. The permutation of the payload data is carried out by a device called an interleaver. In the figure, M is a memory register. The delay line and interleaver force input bits d k to appear in different sequences.
At first iteration, the input sequence d k appears at both outputs of the encoder, x k and y 1k or y 2k due to the encoder's systematic nature.
If the encoders C 1 and C 2 are used respectively in n 1 and n 2 iterations, their rates are respectively equal to. The decoder is built in a similar way to the above encoder. Two elementary decoders are interconnected to each other, but in serial way, not in parallel. The same delay is caused by the delay line in the encoder. DI block is a demultiplexing and insertion module. Consider a memoryless AWGN channel, and assume that at k -th iteration, the decoder receives a pair of random variables:.
Instead of that, a modified BCJR algorithm is used. In order to improve the structure, a feedback loop is used see the dotted line on the figure. The decoder front-end produces an integer for each bit in the data stream. This integer is a measure of how likely it is that the bit is a 0 or 1 and is also called soft bit. This introduces a probabilistic aspect to the data-stream from the front end, but it conveys more information about each bit than just 0 or 1. For example, for each bit, the front end of a traditional wireless-receiver has to decide if an internal analog voltage is above or below a given threshold voltage level.
For a turbo-code decoder, the front end would provide an integer measure of how far the internal voltage is from the given threshold. Both decoders use the sub-block of m likelihoods for the payload data. The decoder working on the second parity sub-block knows the permutation that the coder used for this sub-block.
The key innovation of turbo codes is how they use the likelihood data to reconcile differences between the two decoders. Each of the two convolutional decoders generates a hypothesis with derived likelihoods for the pattern of m bits in the payload sub-block.
The hypothesis bit-patterns are compared, and if they differ, the decoders exchange the derived likelihoods they have for each bit in the hypotheses. Each decoder incorporates the derived likelihood estimates from the other decoder to generate a new hypothesis for the bits in the payload. Then they compare these new hypotheses. This iterative process continues until the two decoders come up with the same hypothesis for the m -bit pattern of the payload, typically in 15 to 18 cycles.
An analogy can be drawn between this process and that of solving cross-reference puzzles like crossword or sudoku. Consider a partially completed, possibly garbled crossword puzzle.
Two puzzle solvers decoders are trying to solve it: To start, both solvers guess the answers hypotheses to their own clues, noting down how confident they are in each letter payload bit.
Then, they compare notes, by exchanging answers and confidence ratings with each other, noticing where and how they differ. Based on this new knowledge, they both come up with updated answers and confidence ratings, repeating the whole process until they converge to the same solution.
Turbo codes perform well due to the attractive combination of the code's random appearance on the channel together with the physically realisable decoding structure.
Turbo codes are affected by an error floor. From an artificial intelligence viewpoint, turbo codes can be considered as an instance of loopy belief propagation in Bayesian networks. From Wikipedia, the free encyclopedia. Archived from the original PDF on 11 June Consultative Committee for Space Data Systems. B1 Data Adaptive Entropy Coder. X band S band K u band K band K a band. Service-oriented architecture Message Abstraction Layer. Retrieved from " https: Error detection and correction Capacity-approaching codes.