R. Ahlswede and J. Korner, Source coding with side information and a converse for degraded broadcast channels, IEEE Transactions on Information Theory 21 (1975), no. 6, 629--637.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....same time it can take the form of cost capacity like problem with nonfixed cost function. Moreover it combines these two problems in a way that is free of the arbitrary nature of both the distortion measure and channel cost. Another formally related problem is source coding with side information[14, 1]. The setting of this problem is very di#erent but the solution happen to be similar. See section 3 for a detailed discussion of this relationship. 1.1 Summary of Results We define the IB coding problem and the IB optimization problem in section 2. We discuss the relationship between the ....

.... since p(y x) in the exponent is defined implicitly in the terms of the assignment mapping p(x x) 3 Relation to Source Coding with Side Information The problem of source coding with side information at the decoder is being studied in the Information Theory community since the mid seventies [14, 1]. It is also known as the Wyner Ahlswede Koroner (WAK) problem. Lately it was discovered [3] that it is closely related to the Information Bottleneck. In order to explore the relations between the two frameworks we first give here a short description of the WAK problem. The WAK framework study ....

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R. F. Ahlswede and J. Korner. Source coding with side information and a converse for degraded broadcast channels. IEEE transaction on information theory, 21(6):629--637, November 1975.

....2 )g [2, 4] See Figure 1. Berger and Yeung [3] found the achievable rate region in the special case where fX k g is discrete and its reconstruction is required to be perfect in the usual Shannon sense. Their result consolidates earlier work of Slepian and Wolf [7] Wyner [8] Ahlswede and Korner [1], Wyner and Ziv [10] and Kaspi and Berger [5] We give the Berger Yeung problem a high resolution interpretation. We assume that X k is real valued, has a smooth conditional distribution given Y k , and is encoded with small mean squared error D x . We determine the asymptotic form of the ....

.... Here fY k g is discrete and D y is small (or zero) The Berger Yeung problem reduces to the Wyner Ziv (WZ) problem [10] for lossy coding of fY k g with perfect side information fX k g) if the rate of the X encoder is greater than H(X) and reduces to the Wyner Ahlswede Korner (WAK) problem [8, 1] (for lossless coding of fX k g with compressed side information on fY k g) if no condition is imposed on the Y distortion (i.e. if D y D y;max ) Likewise, our semi continuous problem gives high resolution (D x 0) interpretations to the WZ and the WAK problems when R 1 RX (D x ) and when D ....

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R. Ahlswede and J. Korner. Source coding with side information and a converse for the degraded broadcast channel. IEEE Trans. Information Theory, 21:629--637, 1975.

....and a single letter characterization of Delta(R) can be found. We then specialize the general Delta(R) to the horse race market. We observe that finding the doubling function for the horse race market can be reduced to source coding with side information of Wyner [26] and Ahlswede Korner [5]. We solve for the doubling function for jointly Gaussian and jointly binary horse race markets. The jointly Gaussian source coding with side information has not been previously treated, since noiseless source coding is unmotivated for continuous random variables. After observing that the doubling ....

....V , like X, is also a discrete random variable. The problem of finding the doubling function in the horse race market can be reduced to that of source coding with side information. Source coding with side information was independently investigated by Wyner [26] and by Ahlswede and Korner [5]. The block diagram for source coding with side information is illustrated in Figure 3.1. Suppose (V i ; X i ) i = 1; n are independent, identically distributed copies of the pair (V; X) The first encoder observes V n and encodes it using R 1 bits symbol. The second encoder observes ....

R. F. Ahlswede and J. Korner. Source coding with side information and a converse for degraded broadcast channels. IEEE Transactions on Information Theory, IT--21:629--637, 1975.

....side information , the maximum increase in the growth rate is given by We then specialize the general to the horse race market. We observe that finding the incremental growth rate for the horse race market can be reduced to source coding with side information of Wyner [22] and Ahlswede Korner [5]. We solve for the incremental growth rate for jointly Gaussian and jointly binary horse race markets. The jointly Gaussian source coding with side information has not been previously treated, since noiseless source coding is unmotivated for continuous random variables. After observing that the ....

....the rate constraint. The problem of finding the incremental growth rate in the horse race market can be reduced to that of source coding with side information. Source coding with side information for discrete random variables was independently investigated by Wyner [22] and by Ahlswede and K orner [5]. The block diagram for source coding with side information is illustrated in Fig. 4. Suppose are independent, identically distributed copies of the pair . The first encoder observes and encodes it using bits per symbol. The second encoder observes and uses bits per symbol to compress it. The ....

R. F. Ahlswede and J. Korner, "Source coding with side information and a converse for degraded broadcast channels," IEEE Trans. Inform. Theory, vol. IT-21, pp. 629--637, 1975.

....and d the exponents of two error probabilities, the probabilities for misacceptance and the probabilities for misrejection. Our analysis has led to a new method for proving converses. Its basis is The Inherently Typical Subset Lemma . It goes considerably beyond the Entropy Characterisation of [2], the Image Size Characterisation of [3] and its extensions in [5] It is conceivable that it has a strong impact on Multi user Information Theory. Key words: Correlated source, identification with fidelity, misacceptance and misrejection error probabilities. I Introduction and Formulation of ....

....case. It turns out that in this special case, R(PX ; P Y ; fi; d) can be expressed in terms of the rate distortion function of the source X. In general, however, the computation of this function may be very difficult. It seems to the authors that there is no easy way to apply the support lemma([2], 5] Chapter 3) to upper bound the cardinality of the set U . Instead, we shall take an alternative approach to the problem. We define for each integer k 1, and any fi 0 R k (PX ; P Y ; fi; d) inffI(X U) U is a r.v. taking k values withE(PXU ; d) fig : 22) For fi = 0, R k (PX ; P Y ; ....

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R. Ahlswede and J. Korner, Source coding with side information and a converse for degrades broadcast channels, IEEE Trans. Inf. Th., Vol. IT-21,629-637, 1975

....one easily sees that I(X Y ) B 2 (X; Y ) min Phi H(X) H(Y ) Psi . A single letter characterisation of the region R 2 is known [3] 4] We give such a characterisation for R 1 (Theorem 2, Section 2) and therefore also for the quantities A 2 (X; Y ) and B 2 (X; Y ) Our method is that of [5], which proves to be quite general and easily adaptable to various source coding problems. The identity R 1 = R 2 follows as a byproduct. During the preparation of this manuscript we learnt that in an independent paper and by a different method Wyner [10] also obtained Theorem 2. In Section 3, ....

....of Fig. 3 is still unsolved. Stating the problem here serves three purposes: 1. It shows the relativity of any notion of common information. 2. The two basic coding theorems for correlated sources, that is, the Slepian Wolf theorem and the source coding theorem in case of side information [5], 10] do not provide all the tools to deal successfully with somewhat more complex networks. Probably the most canonical network of this kind, which is intimately related to the one above, is obtained by considering a correlated source Phi (X i ; Y i ; Z i ) Psi 1 i=1 with three separate ....

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R. Ahlswede and J. K orner, "Source coding with side information and a converse for degraded broadcast channels", IEEE Trans. on Inf. Th., Vol. IT--21, No. 6, 629--637, Nov., 1975.

....by standard analytical methods. The following result of Ahlswede and K orner plays a very important role in reducing an incomputable quantity (region) to a computable one in multi user information theory. It is used in our converse proofs of Theorems 1, 2, and 3. Support Lemma. Lemma 3 of [AK o75] Let f j (j = 1; k) P(Z) R be continuous functions. Then to any PD on the Borel oe algebra of P(Z) there exist k elements P i of P(Z) and non negative numbers ff 1 ; ff k with k P i=1 ff i = 1 such that for every j = 1; k Z P(Z) f j (P ) dP ) k X i=1 ....

....Clearly, the point i R P(Z) f 1 (P ) dP ) R P(Z) f k (dP ) j belongs to the convex closure of J , and thus by the Eggleston Carath eodory theorem (cf. E58] Theorem 18) there are k points in J , say, f(P 1 ) f(P k ) satisfying (2.27) Remarks: 1. Originally, in [AK o75] Carath eodory s theorem was used, which does not require connectedness and gives the weaker conclusion that k 1 instead of k points are needed. 2. Notice that in the proof above only compactness and connectedness of P(Z) was used. Therefore P(Z) can be replaced by any set A with these ....

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Ahlswede, R. and K orner, J. (1975), Source coding with side information and a converse for degraded broadcast channels, IEEE Trans. Inform. Theory 21, 629--637.

No context found.

R. Ahlswede and J. Korner, Source coding with side information and a converse for degraded broadcast channels, IEEE Transactions on Information Theory 21 (1975), no. 6, 629--637.

No context found.

Ahlswede, R., and Korner, J. (1975). \Source coding with side information and a converse for degraded broadcast channels," IEEE Trans. Inform. Theory, 21(6), 629{ 637.

No context found.

R. Ahlswede and J. KSrner, "Source coding with side information and a converse for degraded broadcast channels," IEEE Trans. Inform. Theory, vol. IT-21, no. 6, pp. 629-637, Nov. 1976.

No context found.

R. F. Ahlswede and J. K orner, "Source coding with side information and a converse for degraded broadcast channels," IEEE Trans. Inform. Theory, vol. IT-21, pp. 629--637, Nov. 1975.

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