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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 ]
The LDPC code, in contrast, uses many low depth constituent codes (accumulators) in parallel, each of which encode only a small portion of the input frame. The many constituent codes can be viewed as many low depth (2 state) "convolutional codes" that are connected via the repeat and distribute operations. The repeat and distribute operations ...
To convolutionally encode data, start with k memory registers, each holding one input bit.Unless otherwise specified, all memory registers start with a value of 0. The encoder has n modulo-2 adders (a modulo 2 adder can be implemented with a single Boolean XOR gate, where the logic is: 0+0 = 0, 0+1 = 1, 1+0 = 1, 1+1 = 0), and n generator polynomials — one for each adder (see figure below).
Under this definition codes such as turbo codes, terminated convolutional codes and other iteratively decodable codes (turbo-like codes) would also be considered block codes. A non-terminated convolutional encoder would be an example of a non-block (unframed) code, which has memory and is instead classified as a tree code .
The original information may or may not appear literally in the encoded output; codes that include the unmodified input in the output are systematic, while those that do not are non-systematic. A simplistic example of ECC is to transmit each data bit three times, which is known as a (3,1) repetition code. Through a noisy channel, a receiver ...
A general technique to improve performance is to avoid work. A good example is the use of a fast path for common cases, improving performance by avoiding unnecessary work. For example, using a simple text layout algorithm for Latin text, only switching to a complex layout algorithm for complex scripts, such as Devanagari.
There are many different instances of turbo codes, using different component encoders, input/output ratios, interleavers, and puncturing patterns. 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.
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