Paraunitary Oversampled Filter Bank Design for Channel Coding
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Paraunitary Oversampled Filter Bank Design for Channel Coding Stephan Weiss,1 Soydan Redif,1 Tom Cooper,2 Chunguang Liu,1 Paul D. Baxter,2 and John G. McWhirter2 1 Communications
Research Group, School of Electronics and Computer Science, University of Southampton, Southampton SO17 1BJ, UK 2 Advanced Signal and Information Processing Group, QinetiQ Ltd, Malvern, Worcestershire WR14 3PS, UK Received 20 September 2004; Revised 25 July 2005; Accepted 26 July 2005 Oversampled filter banks (OSFBs) have been considered for channel coding, since their redundancy can be utilised to permit the detection and correction of channel errors. In this paper, we propose an OSFB-based channel coder for a correlated additive Gaussian noise channel, of which the noise covariance matrix is assumed to be known. Based on a suitable factorisation of this matrix, we develop a design for the decoder’s synthesis filter bank in order to minimise the noise power in the decoded signal, subject to admitting perfect reconstruction through paraunitarity of the filter bank. We demonstrate that this approach can lead to a significant reduction of the noise interference by exploiting both the correlation of the channel and the redundancy of the filter banks. Simulation results providing some insight into these mechanisms are provided. Copyright © 2006 Hindawi Publishing Corporation. All rights reserved.
1.
INTRODUCTION
The redundancy and design freedom afforded by oversampled filter banks (OSFBs) has in the past been exploited for robustness towards quantisation of subband signals [1–3], reconstruction of erased or erroneously received subband samples [4, 5], or for the design of error correction coders [6, 7]. More recently, in [8], a systematic parallelism between block codes and oversampled filter bank systems for channel coding has been drawn, whereby the system design is based on unquantised “soft-input” signals [9]. The channel coding schemes in [2, 3, 6–9] are based on an encoding stage using a preset analysis filter bank. The design freedom afforded in the decoding stage formed by the oversampled synthesis filter bank is then utilised to find the solution that reconstructs the signal—either perfectly or in the mean-square error sense—while ideally projecting away from the noise. The filter banks in [6–9] are constructed from FFTs, which leads to low-cost implementations, and have been shown to be very robust towards burst-type errors, and are easily compatible with OFDM-based modulation system. If the additive channel noise is correlated, the projection in [8] is performed in the direction of the principal components of the noise subspace, which ideally is restricted such that a noise-free signal subspace exists. Also, in [6–9], the synthesis design is, despite some degrees of freedom (DOFs) due to oversampling, limited by the a priori choice of the
analysis filter bank. In [10], the synthesis filter bank is given more flexibility by the design aiming at the suppression of the channel noise under the constraint of invertibility, such that an
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