Method of lattice quantization that minimizes storage requirements and computational complexity

摘要

A method of lattice-quantizing an eight-long data point to minimize storage requirements and computational complexity by acquiring the data point, multiplying each coordinate of the data point by the square root of two to form an inflated data point, rounding each coordinate of the rounded and inflated data point to the nearest integer, reducing modulo- two each coordinate of the rounded and inflated data point to form an initial codeword, multiplying a parity-check matrix of an eight-bit Extending 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, creating a signal packet if the codeword does not contain any single-bit errors and double-bit errors, and transmitting the signal packet to a receiver. The receiver receives the signal packet, recovers the intended codeword from the table of sixteen codewords in the Extended Hamming Code, modifies the codeword according to the signal packet in order to recover the rounded and inflated data point, replaces each one in the rounded and inflated data point by the reciprocal of the square root of two of the same polarity, and replaces each two in the rounded and inflated data point by the square root of two of the same polarity in order to recover the data point.