Data-Processing Bounds for Scalar Lossy Source Codes With Side Information at the Decoder

In this paper, we introduce new lower bounds on the distortion of scalar fixed-rate codes for lossy compression with side information available at the receiver. These bounds are derived by presenting the relevant random variables as a Markov chain and applying generalized data-processing inequalities a la Ziv and Zakai. We show that by replacing the logarithmic function with other functions, in the data-processing theorem we formulate, we obtain new lower bounds on the distortion of scalar coding with side information at the decoder. The usefulness of these results is demonstrated for uniform sources and the convex function Q(t)=t1-α, α > 1. The bounds in this case are shown to be better than one can obtain from the Wyner-Ziv rate-distortion function.

[1]  Demosthenis Teneketzis,et al.  On the Structure of Optimal Real-Time Encoders and Decoders in Noisy Communication , 2006, IEEE Transactions on Information Theory.

[2]  Ram Zamir,et al.  Bounds for joint source-channel coding at high SNR , 2011, 2011 IEEE International Symposium on Information Theory Proceedings.

[3]  Michelle Effros,et al.  Quantization as Histogram Segmentation: Optimal Scalar Quantizer Design in Network Systems , 2008, IEEE Transactions on Information Theory.

[4]  Ertem Tuncel,et al.  Low-delay quantization for source coding with side information , 2008, 2008 IEEE International Symposium on Information Theory.

[5]  Ertem Tuncel,et al.  Low-Delay Prediction- and Transform-Based Wyner–Ziv Coding , 2011, IEEE Transactions on Signal Processing.

[6]  Zixiang Xiong,et al.  Successive refinement for the Wyner-Ziv problem and layered code design , 2004, IEEE Transactions on Signal Processing.

[7]  Neri Merhav,et al.  Data Processing Theorems and the Second Law of Thermodynamics , 2010, IEEE Transactions on Information Theory.

[8]  Neri Merhav,et al.  Efficient On-Line Schemes for Encoding Individual Sequences With Side Information at the Decoder , 2009, IEEE Transactions on Information Theory.

[9]  Sergio D. Servetto,et al.  Lattice Quantization With Side Information: Codes, Asymptotics, and Applications in Sensor Networks , 2006, IEEE Transactions on Information Theory.

[10]  Axthonv G. Oettinger,et al.  IEEE Transactions on Information Theory , 1998 .

[11]  Meir Feder,et al.  Distortion lower bounds for finite dimensional joint source-channel coding , 2008, 2008 IEEE International Symposium on Information Theory.

[12]  Neri Merhav,et al.  Structure Theorems for Real-Time Variable Rate Coding With and Without Side Information , 2011, IEEE Transactions on Information Theory.

[13]  Sang Joon Kim,et al.  A Mathematical Theory of Communication , 2006 .

[14]  D. A. Bell,et al.  Information Theory and Reliable Communication , 1969 .

[15]  Zixiang Xiong,et al.  Distributed source coding for sensor networks , 2004, IEEE Signal Processing Magazine.

[16]  J. Kusuma.  Slepian-Wolf Coding and Related Problems , 2022 .

[17]  G. Crooks.  On Measures of Entropy and Information , 2015 .

[18]  Neri Merhav,et al.  On successive refinement for the Wyner-Ziv problem , 2004, IEEE Transactions on Information Theory.

[19]  Ertem Tuncel,et al.  High-resolution predictive Wyner-Ziv coding of Gaussian sources , 2009, 2009 IEEE International Symposium on Information Theory.

[20]  J. Ziv,et al.  A Generalization of the Rate-Distortion Theory and Applications , 1975 .

[21]  Kannan Ramchandran,et al.  Distributed compression for sensor networks , 2001, Proceedings 2001 International Conference on Image Processing (Cat. No.01CH37205).

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

[23]  Ram Zamir,et al.  A Ziv-Zakai-Rényi lower bound on distortion at high resolution , 2008, 2008 IEEE Information Theory Workshop.

[24]  Wei Yu,et al.  Blahut-Arimoto algorithms for computing channel capacity and rate-distortion with side information , 2004, International Symposium onInformation Theory, 2004. ISIT 2004. Proceedings..

[25]  Neri Merhav,et al.  On successive refinement for the Wyner-Ziv problem , 2004, ISIT.

[26]  Jacob Ziv,et al.  On functionals satisfying a data-processing theorem , 1973, IEEE Trans. Inf. Theory.