This paper presents a simple and efficient technique for extending the usefulness of Number Theoretic Transforms(NTTs). The technique is used with Fermat and Mersenne transforms, as well as transforms using general moduli. The constraint on transform length and wordlength is reduced by employing the proposed modified overlap technique, yielding practical architectures for convolution. The proposed technique relies on using transforms of different lengths operating in parallel with output samples time aligned. The usefulness of the technique is illustrated with an application in 2-D optical storage. Optical disks of the future may use a multi-track spiral (with a multi-spot laser) instead of the current single track spiral, yielding increased capacity and transfer speeds. However, this introduces increased complexity in the signal processing blocks, due to the 2 dimensional nature of the read-signals. This paper highlights the benefits of the proposed modified overlap-save method in a 2-D equalizer yielding a significant reduction in complexity compared to conventional equalizer approaches. The reduction is achieved by the novel way in which the transforms are applied and by using Number Theoretic Transforms (NTTs) with the modified overlap method. Despite using very short transform lengths, a significant decrease in computational complexity is still achieved when compared to an equivalent time domain approach. This is achieved through repeated use of the transformed input samples within the multi-track equalizer. A proposed transform domain architecture based on an NTT implementation for 7 rows is detailed.
New efficient structures using the one-hot residue number system (OHRNS) are presented. Normally the RNS uses a binary representation for the residues, though recently there has been renewed interest in the OHRNS, which uses a simple, but novel representation for the residues. The basic component of the OHRNS is the barrel shifter,
making the OHRNS suitable for very high speed applications. The first of the new structures presented reduces the power dissipation in OHRNS adder trees. A modification to the normal barrel shifter is proposed, which reduces the power dissipated by as much as 30%. This improvement is obtained through the use of the modified barrel shifter and the appropriate connection of active-low and active-high stages. This overall power reduction offers the possibility of using the OHRNS in place of a typical full adder based tree in high speed DSP applications. A new storage register for one-hot representations is detailed, which overcomes the problem of having to use a large number of registers. A new architecture is presented for fast OHRNS sign detection. Sign detection is complex and slow to perform in the RNS. A mixed radix conversion (MRC) is typically used for sign detection in the OHRNS. The new sign detection architecture is based on a new property of the Chinese Remainder Theorem (CRT) and is significantly faster than the MRC approach for large moduli sets.
Simulation results using SPICE are detailed for the new structures.