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Error-free code words: aaaabbbbccccddddeeeeffffgggg Interleaved: abcdefgabcdefgabcdefgabcdefg Transmission with a burst error: abcdefgabcd____bcdefgabcdefg Received code words after deinterleaving: aa_abbbbccccdddde_eef_ffg_gg
In a generalization of above concatenation, there are N possible inner codes C in,i and the i-th symbol in a codeword of C out is transmitted across the inner channel using the i-th inner code. The Justesen codes are examples of generalized concatenated codes, where the outer code is a Reed–Solomon code.
The normal memory reads issued by the CPU or DMA devices are checked for ECC errors, but due to data locality reasons they can be confined to a small range of addresses and keeping other memory locations untouched for a very long time. These locations can become vulnerable to more than one soft error, while scrubbing ensures the checking of the ...
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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.
Fig 1 is an example of a SCCC. Fig. 1. SCCC Encoder. The example encoder is composed of a 16-state outer convolutional code and a 2-state inner convolutional code linked by an interleaver. The natural code rate of the configuration shown is 1/4, however, the inner and/or outer codes may be punctured to achieve higher code rates as needed.
Typical implementations use more advanced codes, such as a BCH code, that can correct multiple bits with less overhead. Chipkill is frequently combined with dynamic bit-steering , so that if a chip fails (or has exceeded a threshold of bit errors), another, spare, memory chip is used to replace the failed chip.
Lexicographic code; List decoding; Locally decodable code; Locally recoverable code; Locally testable code; Long code (mathematics) Longitudinal redundancy check; Low-density parity-check code; Luhn algorithm