Patent ID: 8000541

Claim:
A method for approximating sequentially presented numbers (data elements) so that the total amount of information required to approximate the original sequence is less than the total amount of original information, where: i. such data elements ranging from greater than or equal to 0, to less than or equal to 2 m −1, where m is a positive integer greater than 1, and ii. such individual data elements are represented by a base-2 number consisting of no more than m-bits, and iii. the numerical values of the difference between the nth to the n+1th words (n>1) are represented by values ranging from −(2 m −1) to +(2 m −1), comprising the following steps: a. a codebook consisting of a limited set of numbers ranging from −(2 m −1) to +(2 m −1) is created and the values of the numbers in the codebook are associated with a binary code word, such code word consisting of p bits, and subject to p<m, and b. an approximation to the sequence of original data elements (m-bit words) is created by using a computer and by: i. assigning the value of the first data element in the approximation sequence 2 m−1 −1, and ii. constructing the next and each successive data element in the approximation sequence by summing the current data element value in the approximation sequence with one of the available codebook values, such codebook value chosen so that the sum representing the nth data value in the approximation sequence most closely matches the nth data element value in the original sequence, subject to the sum being greater than or equal to 0 and less than or equal to 2 m −1, and iii. the value of the first data element and the ordered sequence of codewords are stored as a representation of the original sequence of numbers, and the reconstruction of the approximation sequence is accomplished by placing the value of 2 m−1 −1 in the first data element position, and each successive data element is reconstructed by adding the numerical value associated with that particular data element's codeword, to the previous numerical value of the approximation sequence.