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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.
In the adjacent diagram, bits 4 and 5 were flipped. This yields only one circle (green) with an invalid parity but the errors are not recoverable. However, the Hamming (7,4) and similar Hamming codes cannot distinguish between single-bit errors and two-bit errors. That is, two-bit errors appear the same as one-bit errors.
A (4,1) repetition (each bit is repeated four times) has a distance of 4, so flipping three bits can be detected, but not corrected. When three bits flip in the same group there can be situations where attempting to correct will produce the wrong code word. In general, a code with distance k can detect but not correct k − 1 errors.
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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.
Reed–Solomon codes are able to detect and correct multiple symbol errors. By adding t = n − k check symbols to the data, a Reed–Solomon code can detect (but not correct) any combination of up to t erroneous symbols, or locate and correct up to ⌊t/2⌋ erroneous symbols at unknown locations.
Cyclic codes are not only simple to implement but have the benefit of being particularly well suited for the detection of burst errors: contiguous sequences of erroneous data symbols in messages. This is important because burst errors are common transmission errors in many communication channels , including magnetic and optical storage devices.
Data Carrier Detect (DCD) or Carrier Detect (CD) is a control signal present inside an RS-232 serial communications cable that goes between a computer and another device, such as a modem. This signal is a simple "high/low" status bit that is sent from a data communications equipment (DCE) to a data terminal equipment (DTE), i.e., from the modem ...