A multivariate polynomial matrix-factorization algorithm is introduced and discussed. This algorithm and another algorithm for computing a globally minimal generating matrix of the syzygy of solutions associated with a polynomial matrix are both associated with a zero-coprimeness constraint that characterizes perfect-reconstruction filter banks. Generalizations, as well as limitations of recent results which incorporate the perfect reconstruction as well as the linear-phase constraints, are discussed with several examples and counterexamples. Specifically, a Gröbner basis-based proof for perfect reconstruction with linear phase is given for the case of two-band multidimensional filter banks, and the algorithm is illustrated by a nontrivial design example. Progress and bottlenecks in the multidimensional multiband case are also reported.Index Terms-Gröbner bases, image compression, multidimensional filter banks.

The aim of this paper is to design sub-optimal 2Dinterleavers and compare the bit error rate (BER) of differentkinds of 2D interleavers in different randomly generatedbursterror environment which are low, medium and high bursterror environment. Typically, low burst error occurs in indoorenvironment and high burst error occurs in outdoorenvironment since transmission scheme in indoor use lessdistance and it is less likely that the line of sight (LOS) isblocked by external objects. This transmission scheme is basedon 2D channel model with 2D linear block codeand 2Dsyndrome decoderpreviously proposed.The proposedinterleavers that we use to compare their performance areblock interleavers, prime interleavers, random interleavers andset partitioning concept interleavers. From the simulationresults, prime interleavers are preferred over theircounterparts since they have relatively lower average (Mean)and standard deviation (SD) of BER

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LEDs can transport the signal or data via visible light instead of radio wave in some place that the radio wave will effect the human or damage the component. Therefore, this paper presents about the digital modulation for improving not only data rate and bit error rate but also flickering, colour rendering, dimming range, luminous efficacy rate that are required to keep in a satisfactory level. There are many types of the modulation that have different property. Therefore, the literature review is discussed and shows the comparison of Return-to-zero On-Off Keying (RZ-OOK), Non-Return-to-zero On-Off Keying (NRZ-OOK), and Binary Phase Shifted Keying (BPSK) in the form of analytical and simulation by the graph of BER versus SNR and also the comparative table of On-Off Keying (OOK), Colour Shifted Keying (CSK), Pulse Position Modulation (PPM), Pulse Width Modulation (PWM), and Orthogonal Frequency Division Multiplexing (OFDM).