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LDPC codes have no limitations of minimum distance, [34] that indirectly means that LDPC codes may be more efficient on relatively large code rates (e.g. 3/4, 5/6, 7/8) than turbo codes. However, LDPC codes are not the complete replacement: turbo codes are the best solution at the lower code rates (e.g. 1/6, 1/3, 1/2). [35] [36]
A typical example of linear code is the Hamming code. Codes defined via a Hamming space necessarily have the same length for every codeword, so they are called block codes when it is necessary to distinguish them from variable-length codes that are defined by unique factorization on a monoid.
The Reed–Solomon code is a [n, k, n − k + 1] code; in other words, it is a linear block code of length n (over F) with dimension k and minimum Hamming distance = + The Reed–Solomon code is optimal in the sense that the minimum distance has the maximum value possible for a linear code of size ( n , k ); this is known as the Singleton bound .
Diagram of a RAID 1 setup. RAID 1 consists of an exact copy (or mirror) of a set of data on two or more disks; a classic RAID 1 mirrored pair contains two disks.This configuration offers no parity, striping, or spanning of disk space across multiple disks, since the data is mirrored on all disks belonging to the array, and the array can only be as big as the smallest member disk.
Viterbi algorithm explanation with the focus on hardware implementation issues. r=1/6 k=15 coding for the Cassini mission to Saturn. Online Generator of optimized software Viterbi decoders (GPL). GPL Viterbi decoder software for four standard codes. Description of a k=24 Viterbi decoder, believed to be the largest ever in practical use.
It is a CSS code (Calderbank-Shor-Steane), using the classical binary [7,4,3] Hamming code to correct for both qubit flip errors (X errors) and phase flip errors (Z errors). The Steane code encodes one logical qubit in 7 physical qubits and is able to correct arbitrary single qubit errors.
Computer programming or coding is the composition of sequences of instructions, called programs, that computers can follow to perform tasks. [1] [2] It involves designing and implementing algorithms, step-by-step specifications of procedures, by writing code in one or more programming languages.
Hamming proposes that Galileo discovered the law of falling bodies not by experimenting, but by simple, though careful, thinking. [11] Hamming imagines Galileo as having engaged in the following thought experiment (the experiment, which Hamming calls "scholastic reasoning", is described in Galileo's book On Motion.):