Method for storage and reconstruction of the extended hamming code for an 8-dimensional lattice quantizer - id: 6404820









A method of lattice-quantizing an eight-long data point to minimize storage requirements by acquiring the data point, multiplying each coordinate of the data point by 2 to form an inflated data point, rounding each coordinate of the rounded and inflated data point to the nearest integer, modulo-two reducing each coordinate of the rounded and inflated data point to form an initial codeword, multiplying a parity-check matrix of an eight-bit Extended Hamming Code by the result of the last step to form a syndrome, correcting any single-bit errors and double-bit errors, if any, in the initial codeword and the rounded and inflated data point, transforming the coordinate system of the initial codeword to an extended quadratic residue form, creating a signal packet, and transmitting the signal packet to a receiver. The receiver receives the signal packet, recovers the intended Extended Hamming Code codeword by a reverse transform of lattice coordinates, modifies the codeword according to the signal packet in order to recover the rounded and inflated data point, replaces each 1 in the rounded and inflated data point by 1/2 of the same polarity, and each 2 by 2 of the same polarity in order to recover the data point.Method for storage and reconstruction of the extended hamming code for an 8-dimensional lattice quantizer640482011/06/200209/07/199920021,068Postol; Michael SamuelUS Patent and Trademark OfficeGoogle Patent Searchpatentimages.storage.googleapis.com/US6404820B1/US06404820-20020611-D00000.pngUniqueinflated data pointsignal packetextended hamming codeinitial codeworddata pointeight-long data pointquadratic residue form8-dimensional lattice quantizermethodpolarity