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2 results about "Circulant matrix" patented technology
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In linear algebra, a circulant matrix is a special kind of Toeplitz matrix where each row vector is rotated one element to the right relative to the preceding row vector. In numerical analysis, circulant matrices are important because they are diagonalized by a discrete Fourier transform, and hence linear equations that contain them may be quickly solved using a fast Fourier transform. They can be interpreted analytically as the integral kernel of a convolution operator on the cyclic group Cₙ and hence frequently appear in formal descriptions of spatially invariant linear operations.
Method and device for encoding and decoding data in communication or broadcasting system
Certain example embodiments may relate to a 5G and / or 6G communication system for supporting higher data transmission rates than 4G communication systems such as LTE. A method performed by a transmitter in a communication system, which method may include: determining the number of input bits; determining a base matrix on the basis of the number of input bits; determining a lifting size (Z) on the basis of at least one of the number of input bits or the base matrix; determining a parity check matrix on the basis of at least one of the base matrix or the lifting size (Z); and performing encoding on the basis of the parity check matrix and the input bits. The size of the parity check matrix is Z×(k+1) Z, the last column block of the parity check matrix corresponds to parity bits, a Z×kZ column block of the parity check matrix corresponds to information word bits, all of modulo-Z values of differences in cyclic shift values corresponding to circulant permutation matrices constituting a Z×Z circulant matrix are different, and all of the circulant matrices corresponding to the information word bits are composed of three or more circulant permutation matrices.
Owner:SAMSUNG ELECTRONICS CO LTD