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Paraunitary Oversampled Filter Bank Design for Channel Coding

Abstract

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.

References

  1. 1.

    Cvetković Z, Vetterli M: Overcomplete expansions and robustness. Proceedings of IEEE-SP International Symposium on Time-Frequency and Time-Scale Analysis (TFTS '96), June 1996, Paris, France 325–328.

    Google Scholar 

  2. 2.

    Bölcskei H, Hlawatsch F: Oversampled filter banks: optimal noise shaping, design freedom, and noise analysis. Proceedings of IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP '97), April 1997, Munich, Germany 3: 2453–2456.

    Google Scholar 

  3. 3.

    Bölcskei H, Hlawatsch F: Noise reduction in oversampled filter banks using predictive quantization. IEEE Transactions on Information Theory 2001, 47(1):155–172. 10.1109/18.904519

    MathSciNet  Article  Google Scholar 

  4. 4.

    Labeau F, Vandendorpe L, Macq B: Structures, factorizations, and design criteria for oversampled paraunitary filterbanks yielding linear-phase filters. IEEE Transactions on Signal Processing 2000, 48(11):3062–3071. 10.1109/78.875464

    Article  Google Scholar 

  5. 5.

    Tanaka T, Yamashita Y: On perfect reconstruction with lost channel data in lapped pseudo-orthogonal transform. Proceedings of 12th European Signal Processing Conference (EUSIPCO '04), September 2004, Vienna, Austria 1: 877–880.

    Google Scholar 

  6. 6.

    Labeau F, Vandendorpe L, Macq B: Oversampled filter banks as error correcting codes. Proceedings of 5th International Symposium on Wireless Personal Multimedia Communications (WPMC '02), October 2002, Honolulu, Hawaii, USA 3: 1265–1269.

    Article  Google Scholar 

  7. 7.

    Labeau F: Design and implementation issues in oversampled filter banks. Proceedings of 36th Asilomar Conference on Signals, Systems, and Computers, November 2002, Pacific Grove, Calif, USA 1: 328–332.

    Google Scholar 

  8. 8.

    Labeau F, Chiang JC, Kieffer M, Duhamel P, Vandendorpe L, Macq B: Oversampled filter banks as error correcting codes: theory and impulse noise correction. IEEE Transactions on Signal Processing 2005, 53(12):4619–4630.

    MathSciNet  Article  Google Scholar 

  9. 9.

    Kliewer J, Mertins A: Error-resilient transmission of waveform signals using overcomplete expansions and soft-input source decoding. Proceedings of 12th European Signal Processing Conference (EUSIPCO '04), September 2004, Vienna, Austria 1: 879–882.

    Google Scholar 

  10. 10.

    Weiss S: On the design of oversampled filter banks for channel coding. Proceedings of 12th European Signal Processing Conference (EUSIPCO '04), September 2004, Vienna, Austria 1: 885–888.

    Google Scholar 

  11. 11.

    McWhirter JG, Baxter PD: A novel technique for broadband singular value decomposition. Proceedings of 12th Annual Workshop on Adaptive Sensor Array Processing (ASAP '04), March 2004, MIT Lincoln Laboratory, Lexington, Mass, USA

    Google Scholar 

  12. 12.

    Kellermann W: Analysis and design of multirate systems for cancellation of acoustical echoes. Proceedings of IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP '88), April 1988, New York, NY, USA 5: 2570–2573.

    Article  Google Scholar 

  13. 13.

    Lorenzelli F, Wang A, Korompis D, Hudson R, Yao K: Subband processing for broadband microphone arrays. The Journal of VLSI Signal Processing—Systems for Signal, Image, and Video Technology 1996, 14(1):43–55. 10.1007/BF00925267

    Article  Google Scholar 

  14. 14.

    Weiss S, Stewart RW, Schabert M, Proudler IK, Hoffman MW: An efficient scheme for broadband adaptive beamforming. Proceedings of 33rd Asilomar Conference on Signals, Systems, and Computers, October 1999, Pacific Grove, Calif, USA 1: 496–500.

    Google Scholar 

  15. 15.

    Neo WH, Farhang-Boroujeny B: Robust microphone arrays using subband adaptive filters. IEE Proceedings—Vision, Image and Signal Processing 2002, 149(1):17–25. 10.1049/ip-vis:20020139

    Article  Google Scholar 

  16. 16.

    Weiss S, Dooley SR, Stewart RW, Nandi AK: Adaptive equalisation in oversampled subbands. IEE Electronics Letters 1998, 34(15):1452–1453. 10.1049/el:19981085

    Article  Google Scholar 

  17. 17.

    Vaidyanathan PP: Multirate Systems and Filter Banks. Prentice-Hall, Englewood Cliffs, NJ, USA; 1993.

    Google Scholar 

  18. 18.

    Harteneck M, Weiss S, Stewart RW: Design of near perfect reconstruction oversampled filter banks for subband adaptive filters. IEEE Transactions on Circuits and Systems—Part II: Analog and Digital Signal Processing 1999, 46(8):1081–1085.

    Article  Google Scholar 

  19. 19.

    Vaidyanathan PP: Theory of optimal orthonormal subband coders. IEEE Transactions on Signal Processing 1998, 46(6):1528–1543. 10.1109/78.678466

    Article  Google Scholar 

  20. 20.

    Redif S, Cooper T: Paraunitary filter bank design via a polynomial singular-value decomposition. Proceedings of IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP '05), March 2005, Philadelphia, Pa, USA 4: 613–616.

    Google Scholar 

  21. 21.

    Papoulis A: Probability, Random Variables, and Stochastic Processes. 3rd edition. McGraw-Hill, New York, NY, USA; 1991.

    Google Scholar 

  22. 22.

    Esmailian T, Kschischang FR, Gulak PG: In-building power lines as high-speed communication channels: channel characterization and a test channel ensemble. International Journal of Communication Systems 2003, 16(5):381–400. 10.1002/dac.596

    Article  Google Scholar 

  23. 23.

    Liu C, Weiss S, Redif S, Cooper T, Lampe L, McWhirter JG: Channel coding for power line communication based on oversampled filter banks. Proceedings of 9th International Symposium on Power-Line Communications and Its Applications (ISPLC '05), April 2005, Vancouver, British Columbia, Canada 246–249.

    Google Scholar 

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Correspondence to Stephan Weiss.

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Weiss, S., Redif, S., Cooper, T. et al. Paraunitary Oversampled Filter Bank Design for Channel Coding. EURASIP J. Adv. Signal Process. 2006, 031346 (2006). https://doi.org/10.1155/ASP/2006/31346

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Keywords

  • Covariance
  • Information Technology
  • Covariance Matrix
  • Gaussian Noise
  • Quantum Information