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...ariable is successively refinable under the Hamming distortion measure [12] and the fact that the refining quantization variables have an additive structure (which can be verified using the method in =-=[13]-=-.) In other words, quantizing Y1 first at rate R1, then subtracting off the quantization variable and further quantizing with R2 yields a final distortion as if Y1 were originally quantized at a rate ...

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...g without excess rate. Indeed, for the special case , this lemma follows immediately from Ahlswede’s classical result [1]. In fact, even for the general case, Ahlswede’s proof technique [1] (also cf. =-=[20]-=-) can be directly applied with no essential change. Note that for the no excess rate case, the two descriptions are (approximately) independent (see (3.4) in [1]). It is easy to verify that this (appr...

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...nt codes, are multiple-description codes used as MRSCs. The th-resolution reproduction of an AMRSC equals the sum of the independent reconstructions from the multiple description code’s first packets =-=[15]-=-. A two-stage AMRSC (A2RSC) encodes source using two packets with rates and , respectively. The reproduction from packet has expected distortion , and the sum of the reproductions from both packets yi...

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...ed. This source coding scenario has been extensively studied in the last two decades by Koshelev [7], Equitz and Cover [6], Rimoldi [10], Effros [3], [4], Lastras and Berger [8], Tuncel and Rose [11]–=-=[13]-=-, and many others. Among the most popular questions is whether a given source is successively refinable at the prescribed distortion levels, i.e., whether it is possible to achieve the single resoluti...

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... + R2 = R(R1, D {1}, D {1,2})}. Proof: It is worth noting that this problem is not identical to multiple description coding without excess rate. Nevertheless, Ahlswede’s proof technique [1] (also cf. =-=[20]-=-) can be directly applied here with no essential change. The details are omitted. Let R(D) denote the rate-distortion function, i.e., R(D) = min p ˆX|X :E[d(X, ˆ I(X; X)]≤D ˆ X). Now we proceed to stu...

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...f early works [1]–[3]. The rate-distortion problem with various extensions has subsequently been thoroughly researched, among which are the notable works by Effros [4], [5] and by Tuncel and Rose [6]–=-=[8]-=-. The successive refinement coding structure is clearly appealing in multimedia delivery systems, since such a framework allows a single copy of the multimedia content on the server to satisfy the req...

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...Sincesis statistically independent ¡ ofs� , or equivalently, � � ��� and given by , ���s¡ ,s�s¡ � �s�s¡ � � ¢s, and the enhancement layer provides no information about the core layer. Tuncel and Rose =-=[20]-=- show that this condition is satisfied for additive successive refinement. Thus, even though the enhancement layer is sent in-the-clear, the eavesdropper gains no advantage, and the secrecy of the sys...

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...non’s rate distortion theorem for white Gaussian sources [1]. At the same time, the representation method gives a very simple proof of successive refinability [4] and additive successive refinability =-=[5]-=- of white Gaussian sources under the mean squared error distortion. It turns out that the asymptotic distortion in Theorem 1, which is achieved by the simple successive representation method, is in fa...

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...e problem of scalable distributed source coding (S-DSC) or successive refinement of distributed correlated sources, which generalizes the traditional problem of scalable coding of a single source [6]–=-=[9]-=-. 2 Successive refinement for Wyner–Ziv coding (side information at the decoder) was proposed in [10], and has been studied in [10] and [11] from the information-theoretic perspective of characterizin...

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...he signal, the error, the error of the error, etc. recursively. This representation method, incidentally, gives a very simple proof of successive refinability [7] and additive successive refinability =-=[15]-=- of white Gaussian sources under the mean squared distortion. II. PROOF SKETCH OF THEOREM 1 Define R(δ) = (1/2) log(1/δ) for 0 < δ < 1 and let R > R(δ). We recall that a random codebook (dictionary) C...