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Unformatted text preview: Source Coding with Decoder Side Information Presenter: Shivaprasad Kotagiri. Date: 27 September 2006. Reading: Elements of Information theory by Cover & Thomas [1, Secs 14.8 and 14.9] and Wynerziv paper [2] 1 Introduction In this report, we study source coding problems with decoder side information (SI). Source coding problems with decoder side information are a special case of distributed source coding problems. We outline the relation between various distributed source coding problems in Table 1 with the help of Figure 1. For reference, we also include the standard singlesource lossless and lossy compression problems in Table 1. We discuss source coding problems with decoder SI in which an encoder maps a random vector x n 1 from a random source x to w ∈ W = { 1 , 2 , . . . , M } , and a decoder, provided with w and the side information correlated with x n , computes an estimate of x n 1 subject to a fidelity criterion 1 . In general, the correlated information that is available at the decoder is called as side information. A B EncoderX EncoderY Decoder x n y n w x w y Output Figure 1: Block diagram of distributed source coding. The basic idea of source coding with decoder SI is to encode the conditional un certainity in x n given the side information. In this report, we study the rate at which a source can be compressed wiht the side information at the decoder to achieve some specified distortion D x under a given distortion measure d ( · , · ). Let us denote the rate of codes used in EncoderX and EncoderY as R x and R y , respectively. In this paper, we are interested in two source coding problems when switch B is closed in Figure 1. In these problems, y n is correlated with x n , the side information available to the decoder 1 In this report, we use the following notation: xrandom variable, xsample value of rv x , x n = ( x 1 , x 2 , . . . , x n ) n length random vector, x nsample vector of x n , X the alphabet set from which x takes vales, In general, we omit the subscripts of probability distribution functions (pdfs), i.e., p ( x ) = p x ( x ) Type of coding R y (A,B) ( D x , D y ) Dec. O/p Reference Lossless source coding (of x n ) N/A (0 , 0) (0, N/A) ˆ x [1] Lossy source coding (SC) (of x n ) N/A (0 , 0) ( ≥ 0, N/A) ˆ x [1] SlepianWolf coding ≤ H ( y ) (0 , 1) (0,0) (ˆ x n , ˆ y n ) [1, 3] Lossy multiterminal source coding ≤ H ( y ) (0 , 1) ( ≥ , ≥ 0) (ˆ x n , ˆ y n ) [4] Conditional RateDistortion ≥ H ( y ) (1 , 1) ( ∞ , ∞ ) ˆ x n [5] Lossless SC with Lossy SI ≤ H ( y ) (0 , 1) (0 , ∞ ) ˆ x n [1, 6] Lossy SC with Lossless SI ≥ H ( y ) (0 , 1) ( ≥ , ∞ ) ˆ x n [1, 2] Table 1: Comparison of several problems obtained via different switch configurations in Figure 1. Column 2 indicates whether lossy or lossless side information is available at the decoder. Column 3 indicates which switches are closed. If switch variable is , then it is open. Otherwise, it is closed. Column 4 indicates distortion constraints on the decoderis open....
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This note was uploaded on 02/05/2012 for the course EE EE308 taught by Professor B.k.dey during the Spring '09 term at IIT Bombay.
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