Processor Architectures for Two-Dimensional Convolvers Using a Single Multiplexed Computational Element with Finite Field Arithmetic

Efficient number theoretic transforms for convolutions using ROM arrays

“…From the practical point of view, the proposed method requires a small number of additions per point and the memory required is much less than previous reported methods (Jullien and Miller 1980, Nagpal et al 1983, Rice 1979. Furthermore, due to the similarities between modules and because of the fact that exactly the same processes are required for different dimensions, the control of data flow is extremely simple and the whole computation can be done in place and in order.…”

“…Nagpel et al (1983) have recently modified this technique by using only moduli of the form (4k + I), rather than using the second degree Galois field. However, their method still requires a very large ROM size (Jullien and Miller 1980, Nagpal et al 1983, Rice 1979) and a relatively complicated technique for the computation involving multiplications by powers of a (the root of unity) has been used.…”

“…The choice of N can significantly affect the number of operations of the NIT. Previously, the main concern of other authors has been to look for transform lengths of powers of two (Agarwal and Burrus 1974, Jullien and Miller 1980, Nagpal et al 1983, Rice 1979. However, if we use look-up tables stored in ROMs to implement the multiplication by an, where n = 1, 2, ..., N -1, the ROM size becomes too large for practical realisation in most cases.…”

“…However, if we use look-up tables stored in ROMs to implement the multiplication by an, where n = 1, 2, ..., N -1, the ROM size becomes too large for practical realisation in most cases. An alternative approach is to use indices and submodular decompositions to produce a manageable ROM size and hardware (Jullien and Miller 1980, Nagpal et al 1983). This approach is still relatively complicated and extra steps are necessary to carry out the conversion.…”

Error Detection & Correction in Wireless Sensor Networks By Using Residue Number Systems

“…The system also offers some useful properties for error detection, error correction and fault tolerance in digital systems. [11], [12], [13], [14] direct digital frequency synthesis [15]. A residue number system is defined by a set of relative prime numbers, {m 1 , m 2 , …, m r } called the "moduli".…”