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Published in Philip A. Laplante, Comprehensive Dictionary of Electrical Engineering, 2018
correlator a circuit that calculates the correlation function. See also correlation function. correspondence problem the problem of matching points in one image with their corresponding points in a second image. corresponding point a point, in a set of images representing a different view of the same scene, onto which the same physical point in the real world is projected. corrugated horn a horn with grooves on its inner walls. The grooves create the same boundary conditions on all four walls of the horn. This results in the elimination of spurious diffraction at the edges of the horn aperture. coset leader each possible error pattern of the code word representing the left-most column of the standard array.
An Introduction to Error-Correcting Codes
Published in Erozan M. Kurtas, Bane Vasic, Advanced Error Control Techniques for Data Storage Systems, 2018
(d,k) subcode of a linear block code. The modulation code is treated as a subcode of the error correcting code (a Hamming code), and they find a subcode of an error correcting code satisfying the additional (d,k) constraints required. They do this by selecting the coset in the standard array of Hamming codes which has the maximum number of (d,k) constrained sequences. This approach requires modulation codes that have very large block sizes when compared to conventional modulation codes in practice. One advantage of this scheme is that off-the-shelf decoders can be used. Systematic (but suboptimum) subcodes are also presented. In a similar approach, Liu and Lin [72] describes a class of (d,k) block codes with minimum Hamming distance of 3 based on dklr sequences (the l and r represent the maximum number of consecutive zeros at the beginning and end of a (d,k)-sequence respectively) and cyclic Hamming codes. A codeword in the constructed code is formed by two subblocks satisfying the dklr constraint. One is the message subblock and the other is the parity check subblock.
Introduction to Coding Theory
Published in R. Balakrishnan, Sriraman Sridharan, Discrete Mathematics, 2019
R. Balakrishnan, Sriraman Sridharan
Figure 5.3 gives the standard array for the decode!standard array code H3. If u is the message vector (that is, codeword) and v is the received vector, then v − u = e is the error vector. If we assume that v has one or no error, then e is of weight 1 or 0. Accordingly e is a coset leader of the standard array. Hence to get u from v, we subtract e from v. In the binary case (as −e = e), u = v + e. For instance, if in Figure 5.3, v = 1100110, then v is present in the second coset for which the leader is e = 1000000. Hence the message is u = v + e = 0100110. This incidentally shows that H3 can correct single errors. However, if for instance, u = 0100110 and v = 1000110, then e = 1100000 is of weight 2 and is not a coset leader of the standard array of Figure 5.3. In this case, the standard array decoding of H3 will not work as it would wrongly decode v as 1000110−0000001=1000111∈H3. (Notice that v is present in the last row of Figure 5.3). The error is due to the fact that v has two errors and not just one. Standard array decoding is therefore maximum likelihood decoding.
An efficient and improved PTS algorithm for PAPR reduction in OFDM system
Published in International Journal of Electronics, 2022
Prabal Gupta, H. Pal Thethi, Ajay Tomer
Coset leaders are the left most column in standard array and they are shown by . We have used Bose Chaudhuri Hocquenghem (BCH) codes where is information bit length and block length is represented by for encoding process. All the absolutely valid codewords that is always follows with as parity check matrix. The particular vector which belongs to has same syndrome as the vector .