Optimal multiresolution quantization for broadcast channels with random index assignment

This paper studies the design and analysis of multiresolution vector quantization (MRVQ) for broadcast channels. Given a broadcast system with MRVQ, a random index assignment, and a coded broadcast channel, we first obtain a closed-form formula for the weighted end-to-end distortion (EED) of the system. Based on the formula, an iterative algorithm is then proposed for designing optimal MRVQ for the broadcast system. Experimental results demonstrate that multiresolution quantizers jointly designed with channel conditions by the proposed algorithm significantly reduce the weighted EED in comparison with multiresolution quantizers designed without reference to channel conditions.

[1]  R. Gallager Information Theory and Reliable Communication , 1968 .

[2]  K. Zeger,et al.  Asymptotic Bounds on Optimal Noisy Channel QuantizationVia Random Coding , 1994 .

[3]  Nariman Farvardin,et al.  Fixed-rate successively refinable scalar quantizers , 1996, Proceedings of Data Compression Conference - DCC '96.

[4]  Kenneth Zeger,et al.  Quantizers with uniform encoders and channel optimized decoders , 2004, IEEE Transactions on Information Theory.

[5]  Joseph M. Kahn,et al.  Transmission of analog signals using multicarrier modulation: a combined source-channel coding approach , 1996, IEEE Trans. Commun..

[6]  Allen Gersho,et al.  Pseudo-Gray coding , 1990, IEEE Trans. Commun..

[7]  Allen Gersho,et al.  Vector quantization and signal compression , 1991, The Kluwer international series in engineering and computer science.

[8]  Nariman Farvardin,et al.  On the performance and complexity of channel-optimized vector quantizers , 1991, IEEE Trans. Inf. Theory.

[9]  Andrea J. Goldsmith,et al.  Joint design of fixed-rate source codes and multiresolution channel codes , 1998, IEEE Trans. Commun..

[10]  Kenneth Rose,et al.  Vector quantization with transmission energy allocation for time-varying channels , 1999, IEEE Trans. Commun..

[11]  Robert M. Gray,et al.  Joint source and noisy channel trellis encoding , 1981, IEEE Trans. Inf. Theory.

[12]  Michelle Effros Robustness to channel variation in source coding for transmission across noisy channels , 1997, 1997 IEEE International Conference on Acoustics, Speech, and Signal Processing.

[13]  Aaron D. Wyner,et al.  Coding Theorems for a Discrete Source With a Fidelity CriterionInstitute of Radio Engineers, International Convention Record, vol. 7, 1959. , 1993 .

[14]  William Equitz,et al.  Successive refinement of information , 1991, IEEE Trans. Inf. Theory.

[15]  Nariman Farvardin,et al.  Joint design of block source codes and modulation signal sets , 1992, IEEE Trans. Inf. Theory.

[16]  Michelle Effros Distortion-rate bounds for fixed- and variable-rate multiresolution source codes , 1999, IEEE Trans. Inf. Theory.

[17]  Kenneth Zeger,et al.  Quantizers with uniform decoders and channel-optimized encoders , 2006, IEEE Transactions on Information Theory.

[18]  Thomas R. Crimmins,et al.  Minimization of mean-square error for data transmitted via group codes , 1969, IEEE Trans. Inf. Theory.

[19]  Kenneth Zeger,et al.  Randomly Chosen Index Assignments Are Asymptotically Bad for Uniform Sources , 1999, IEEE Trans. Inf. Theory.

[20]  Michelle Effros,et al.  Multiresolution vector quantization , 2004, IEEE Transactions on Information Theory.

[21]  En-Hui Yang,et al.  Optimal quantization for noisy channels with random index assignment , 2008, 2008 IEEE International Symposium on Information Theory.

[22]  Stephen P. Boyd,et al.  Convex Optimization , 2004, Algorithms and Theory of Computation Handbook.

[23]  Joel Max,et al.  Quantizing for minimum distortion , 1960, IRE Trans. Inf. Theory.

[24]  Michelle Effros Practical multi-resolution source coding: TSVQ revisited , 1998, Proceedings DCC '98 Data Compression Conference (Cat. No.98TB100225).

[25]  David L. Neuhoff,et al.  Optimal binary index assignments for a class of equiprobable scalar and vector quantizers , 1995, IEEE Trans. Inf. Theory.

[26]  Joseph M. Kahn,et al.  Combined source-channel coding using channel-optimized quantizer and multicarrier modulation , 1996, Proceedings of ICC/SUPERCOMM '96 - International Conference on Communications.

[27]  Kenneth Zeger,et al.  Binary Lattice Vector Quantization with Linear Block Codes and Affine Index Assignments , 1998, IEEE Trans. Inf. Theory.

[28]  S. P. Lloyd,et al.  Least squares quantization in PCM , 1982, IEEE Trans. Inf. Theory.

[29]  Kannan Ramchandran,et al.  Multiresolution joint source-channel coding using embedded constellations for power-constrained time-varying channels , 1996, 1996 IEEE International Conference on Acoustics, Speech, and Signal Processing Conference Proceedings.

[30]  Masao Kasahara,et al.  A construction of vector quantizers for noisy channels , 1984 .

[31]  J. W. Modestino,et al.  Combined Source-Channel Coding of Images , 1978, IEEE Trans. Commun..

[32]  Roar Hagen,et al.  Robust Vector Quantization by a Linear Mapping of a Block Code , 1999, IEEE Trans. Inf. Theory.

[33]  NARIMAN FARVARDIN,et al.  Optimal quantizer design for noisy channels: An approach to combined source - channel coding , 1987, IEEE Trans. Inf. Theory.

[34]  Nariman Farvardin,et al.  A study of vector quantization for noisy channels , 1990, IEEE Trans. Inf. Theory.

[35]  Sorina Dumitrescu,et al.  Algorithms for optimal multi-resolution quantization , 2004, J. Algorithms.

[36]  Thomas M. Cover,et al.  Elements of Information Theory , 2005 .