Multiplication of integral octonions

Abstract

Communicated by I. P. ShestakovThe integral subsets of octonions are an analog of integers in real numbers and related to many interesting topics in geometry and physics via E 8 -lattices. In this paper, we study the properties of the multiplication of the integral subsets of octonions by studying configuration of Fano plane via blocks and operations on them. And we show that the integral subsets are integral indeed by introducing new and elementary methods.

An ant colony optimization aided two-dimensional soft output viterbi algorithm detection scheme for holographic data storage systems

“…Figure 3 shows the BER curves of the conventional and proposed detection schemes when the grade of blur is 1.6. The 2D SOVA detection scheme 18) has more than 2 dB gains than the 1D PRML detection scheme 12) by averaging the outputs of the horizontal and vertical 1D SOVA detectors at the BER of 10 −4 . The 2D PRML detection scheme 16) using the 2D PR target has more than 0.5 dB gains than the 2D SOVA detection scheme.…”

“…5,6) Therefore, more powerful signal processing techniques are necessarily required to achieve high-density recording in HDS systems. [7][8][9][10][11] Various detection schemes [12][13][14][15][16][17][18][19][20][21][22] have been introduced for HDS systems. A one-dimensional (1D) partial response maximum likelihood (PRML) detection scheme using a 2D equalizer with a 1D partial response (PR) target was proposed in Ref.…”

“…A one-dimensional (1D) partial response maximum likelihood (PRML) detection scheme using a 2D equalizer with a 1D partial response (PR) target was proposed in Ref. 12. By using the 1D PR target, the bit error rate (BER) performances of the 1D PRML detection scheme is severely degraded as 2D ISI increases.…”