Simultaneous CDMA and error correction schemes based on wavelet filters in integer quotient rings

Kuen-Tsair Lay; Lin-Wen Kong; Jiann-Horng Chen

doi:10.1117/12.381693

5 April 2000 Simultaneous CDMA and error correction schemes based on wavelet filters in integer quotient rings

Kuen-Tsair Lay, Lin-Wen Kong, Jiann-Horng Chen

Proceedings Volume 4056, Wavelet Applications VII; (2000) https://doi.org/10.1117/12.381693
Event: AeroSense 2000, 2000, Orlando, FL, United States

Abstract

In the past decade, wavelet filters have been widely applied to signal processing. In effect, wavelet filters are perfect reconstruction filter banks (PRFBs). However, in most researches, the filterbanks and wavelets operate on real- valued or complex-valued signals. In this paper, PRFBs operating over integer quotient rings (IQRs) are introduced. We denote an IQR as Z/(q). Algorithms for constructing such filter banks are proposed. The PRFB design can be carried out either in the time or the frequency domain. We demonstrate that some classical or well known filter tap coefficients can even be transformed into values over Z/(q) in a simple and straightforward way. Here we emphasize that to achieve perfect reconstruction (PR), the filters need not to work on elements in fields. In fact, operating on elements in IQRs can achieve PR with proper choices of a ring and filter tap coefficients. The designed filter banks can be orthogonal or biorthogonal. Based ona PRFB over an IQR, to which we refer as an IQR-PRFB, a perfect reconstruction transmultiplexer (PRTM), to which we refer as an IQR-PRTM, can be derived. Through the utilization of the IQR-PRTM multiplexing and multiple access in a multi-user digital communication system can be realized. The IQR-PRTM effectively decomposes the communication signal space into several orthogonal subspaces, where each multiplexed user sends his message in one of them. If some of the orthogonal subspaces are preserved for parity check, then error correction at the receiving end can be performed. In the proposed schemes, the data to be transmitted must be represented with elements of Z/(q), which can be done easily. A modulation and demodulation/detection scheme, in conjunction with the IQR-PRTM is proposed.

Citation Download Citation

Kuen-Tsair Lay, Lin-Wen Kong, and Jiann-Horng Chen "Simultaneous CDMA and error correction schemes based on wavelet filters in integer quotient rings", Proc. SPIE 4056, Wavelet Applications VII, (5 April 2000); https://doi.org/10.1117/12.381693

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