China
Africa
Explore chapters and articles related to this topic
DTN Coding
Published in Aloizio Pereira da Silva, Scott Burleigh, Katia Obraczka, Delay and Disruption Tolerant Networks, 2019
Marius Feldmann, Felix Walter, Tomaso de Cola, Gianluigi Liva
The generator matrix is in systematic form, which readily yields the parity-check matrix H=(111010011010101011001)
Space Time Block Coded MIMO Systems
Published in Brijesh Kumbhani, Rakhesh Singh Kshetrimayum, MIMO Wireless Communications over Generalized Fading Channels, 2017
Brijesh Kumbhani, Rakhesh Singh Kshetrimayum
As in the case of error correcting codes, generator matrix is designed to introduce redundancy such that the resulting codeword system becomes capable of correcting errors as per the design. In the same way, STBC generator matrix introduces redundancy to achieve diversity gain in turn that reduces the error probabilities at greater rates with increasing SNR. Here, let us compare the matrices obtained for equivalent channel coefficients in equation (6.34) and the actual Alamouti STBC codeword. Heq=[h11h12h12*-h11*]X=[s1-s2*s2s1*]
Additive codes and network codes
Published in Jürgen Bierbrauer, Introduction to Coding Theory, 2016
A generator matrix G of a q-linear [n, k]qm code is a (km, n) matrix with entries from E = Fqm whose rows form an Fq basis of the code (the codewords are the Fq-linear combinations of the rows of G). A check matrix is a generator matrix of the dual code. Observe here that km is of course an integer, but k need not be integer.
Distributed polar-coded OFDM based on Plotkin’s construction for half duplex wireless communication
Published in International Journal of Electronics, 2018
Rahim Umar, Fengfan Yang, Shoaib Mughal, HongJun Xu
where , are two linear block codes of same length such as , ‘’ is a modulo 2 sum operation. The resulted code word has a dimension , code word length , code rate and minimum hamming distance. The most interesting point regarding code word is the fact that it can also be obtained using the following generator matrix
A Quantum Resistant Chameleon Hashing and Signature Scheme
Published in IETE Journal of Research, 2022
A linear code C is a k-dimensional linear subspace of and all the elements of C are called codewords. The weight of an element x in is the number of nonzero coordinates of x . The minimum distanced of a linear code is the minimum weight of any nonzero element of the code. A code is specified either by a generator matrix G or by a parity check matrix H. A generator matrix of a linear code C is a matrix G whose row vectors form a basis for the vector subspace C, i.e.,. A parity-check matrixH of a linear code C is an matrix whose row vectors form a basis for the orthogonal complement of the vector subspace C. Hence . The syndrome of a word by H is a vector defined by . If the error correcting capability of the code is then for any syndrome s, there is at most one word of weight , such that . If there exists a word x corresponding to a vector , then s is said to be t-decodable (or simply decodable) in the code defined by H. Given a random syndrome s, finding whether s is t-decodable in the code defined by a random matrix H has been proved to be NP-complete [16]. Decoding can be easily performed for more structured codes.