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Low-density parity-check (LDPC) codes are a class of highly efficient linear block codes made from many single parity check (SPC) codes. They can provide performance very close to the channel capacity (the theoretical maximum) using an iterated soft-decision decoding approach, at linear time complexity in terms of their block length.
In 2003, an irregular repeat accumulate (IRA) style LDPC code beat six turbo codes to become the error-correcting code in the new DVB-S2 standard for digital television. [13] The DVB-S2 selection committee made decoder complexity estimates for the turbo code proposals using a much less efficient serial decoder architecture rather than a ...
Dynamic random-access memory (DRAM) may provide stronger protection against soft errors by relying on error-correcting codes. Such error-correcting memory, known as ECC or EDAC-protected memory, is particularly desirable for mission-critical applications, such as scientific computing, financial, medical, etc. as well as extraterrestrial ...
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. For example, an overall code rate of 1/2 may be achieved by puncturing the outer convolutional code to rate 3/4 and the inner convolutional code to rate 2/3.
The first public paper on turbo codes was "Near Shannon Limit Error-correcting Coding and Decoding: Turbo-codes". [4] This paper was published 1993 in the Proceedings of IEEE International Communications Conference. The 1993 paper was formed from three separate submissions that were combined due to space constraints.
The main idea is to choose the error-correcting bits such that the index-XOR (the XOR of all the bit positions containing a 1) is 0. We use positions 1, 10, 100, etc. (in binary) as the error-correcting bits, which guarantees it is possible to set the error-correcting bits so that the index-XOR of the whole message is 0.
The most popular erasure codes are Reed-Solomon coding, Low-density parity-check code (LDPC codes), and Turbo codes. [ 1 ] As of 2023, modern data storage systems can be designed to tolerate the complete failure of a few disks without data loss, using one of 3 approaches: [ 2 ] [ 3 ] [ 4 ]
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] This design has a better performance than any previously conceived concatenated codes.