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In computer networking, linear network coding is a program in which intermediate nodes transmit data from source nodes to sink nodes by means of linear combinations. Linear network coding may be used to improve a network's throughput, efficiency, and scalability , as well as reducing attacks and eavesdropping.
The codewords in a linear block code are blocks of symbols that are encoded using more symbols than the original value to be sent. [2] A linear code of length n transmits blocks containing n symbols. For example, the [7,4,3] Hamming code is a linear binary code which represents 4-bit messages using 7-bit codewords. Two distinct codewords differ ...
A linear encoder is a sensor, transducer or readhead paired with a scale that encodes position. The sensor reads the scale in order to convert the encoded position into an analog or digital signal , which can then be decoded into position by a digital readout (DRO) or motion controller.
Latin square based code for non-white noise (prevalent for example in broadband over powerlines) Lexicographic code; Linear Network Coding, a type of erasure correcting code across networks instead of point-to-point links; Long code; Low-density parity-check code, also known as Gallager code, as the archetype for sparse graph codes
Examples of block codes are Reed–Solomon codes, Hamming codes, Hadamard codes, Expander codes, Golay codes, Reed–Muller codes and Polar codes. These examples also belong to the class of linear codes, and hence they are called linear block codes. More particularly, these codes are known as algebraic block codes, or cyclic block codes ...
A convolutional encoder is a discrete linear time-invariant system. Every output of an encoder can be described by its own transfer function, which is closely related to the generator polynomial. An impulse response is connected with a transfer function through Z-transform. Transfer functions for the first (non-recursive) encoder are:
The receiver is designed so that either code word of the pair decodes to the same data bits. Examples include alternate mark inversion, Differential Manchester encoding, coded mark inversion and Miller encoding. differential coding each symbol relative to the previous symbol. Examples include MLT-3 encoding and NRZI.
An (,) quasi-cyclic code is a linear block code such that, for some which is coprime to , the polynomial () is a codeword polynomial whenever () is a codeword polynomial. Here, codeword polynomial is an element of a linear code whose code words are polynomials that are divisible by a polynomial of shorter length called the generator polynomial .
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