Multi-track NTT equalizer for optical storage

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.