The Explicit Coding Rate Region of Symmetric Multilevel Diversity Coding

Guo, Tao; Yeung, Raymond W.

doi:10.1109/isit.2018.8437867

Cited by 2 publications

(13 citation statements)

References 3 publications

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“…This is currently under our investigation. APPENDIX A SOME LEMMAS/THEOREMS FROM [3], [4] In the following lemmas and theorem, we assume [3]: Let {c(v)} be an optimal α-resolution for λ. Then there exists 0 ≤ l ≤ α − 1 such that λ i − λi > 0 if and only if 1 ≤ i ≤ l. Lemma 4 in [3]:…”

Section: Discussionmentioning

confidence: 99%

“…We first present an example that motivates the general group pairwise coding scheme. 4), and p = 11. The security constraint for the (4, 3) DS-SMDC problem should be (N 1 , N 2 , N 3 , N 4 ) = (0, 1, 2, 0).…”

Section: B Rate Region Of Ds-smdcmentioning

confidence: 92%

“…Similar to Lemma 6 in [4], the following lemma gives a sufficient condition of redundancy in the characterization of the rate region.…”

Section: Appendix E Converse Proof Of Theorem 2 (Continuing)mentioning

confidence: 94%

“…Furthermore, an α-resolution is called optimal if it achieves the optimal value f α (λ). In the following proof, we will take advantage of some lemmas and theorems from [3] and [4], which are enclosed in Appendix A for convenience.…”

Section: Converse Proof Of Theoremmentioning

confidence: 99%

“…It was shown [1], [3] that separately encoding these independent messages, referred to as superposition coding, is optimal in terms of achieving the entire rate region. The characterization of the coding rate region therein involves implicit and uncountably many inequalities, and an explicit characterization of the coding rate region was recently obtained [4]. The problem has also been extended and generalized, e.g., to allow node regeneration [5] and to allow asymmetric decoders [6].…”

Section: Introductionmentioning

confidence: 99%

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Weakly Secure Symmetric Multilevel Diversity Coding

Guo

Tian

et al. 2019

2019 IEEE Information Theory Workshop (ITW)

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Multilevel diversity coding is a classical coding model where multiple mutually independent information messages are encoded, such that different reliability requirements can be afforded to different messages. It is well known that superposition coding, namely separately encoding the independent messages, is optimal for symmetric multilevel diversity coding (SMDC) (Yeung-Zhang 1999). In the current paper, we consider weakly secure SMDC where security constraints are injected on each individual message, and provide a complete characterization of the conditions under which superposition coding is sumrate optimal. Two joint coding strategies, which lead to rate savings compared to superposition coding, are proposed, where some coding components for one message can be used as the encryption key for another. By applying different variants of Han's inequality, we show that the lack of opportunity to apply these two coding strategies directly implies the optimality of superposition coding. It is further shown that under a set of particular security constraints, one of the proposed joint coding strategies can be used to construct a code that achieves the optimal rate region.

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Section: Discussionmentioning

confidence: 99%

Section: B Rate Region Of Ds-smdcmentioning

confidence: 92%

“…Similar to Lemma 6 in [4], the following lemma gives a sufficient condition of redundancy in the characterization of the rate region.…”

Section: Appendix E Converse Proof Of Theorem 2 (Continuing)mentioning

confidence: 94%

Section: Converse Proof Of Theoremmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Weakly Secure Symmetric Multilevel Diversity Coding

Guo

Tian

et al. 2019

2019 IEEE Information Theory Workshop (ITW)

Self Cite

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The Explicit Coding Rate Region of Symmetric Multilevel Diversity Coding

Guo

Yeung

2018

2018 Information Theory and Applications Workshop (ITA)

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It is well known that superposition coding, namely separately encoding the independent sources, is optimal for symmetric multilevel diversity coding (SMDC) (Yeung-Zhang 1999) for any L ≥ 2, where L is the number of levels of the coding system. However, the characterization of the coding rate region therein involves uncountably many linear inequalities and the constant term (i.e., the lower bound) in each inequality is given in terms of the solution of a linear optimization problem. Thus this implicit characterization of the coding rate region does not enable the determination of the achievability of a given rate tuple. In principle, the achievability of a given rate tuple can be determined by direct computation, but the complexity is prohibitive even for L = 5. In this paper, for any fixed L, we obtain in closed form a finite set of linear inequalities for characterizing the coding rate region. We further show by the symmetry of the problem that only a much smaller subset of this finite set of inequalities needs to be verified in determining the achievability of a given rate tuple. Yet, the cardinality of this smaller set grows at least exponentially fast with L. We also present a subset entropy inequality, which together with our explicit characterization of the coding rate region, is sufficient for proving the optimality of superposition coding.

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The Explicit Coding Rate Region of Symmetric Multilevel Diversity Coding

Cited by 2 publications

References 3 publications

Weakly Secure Symmetric Multilevel Diversity Coding

Weakly Secure Symmetric Multilevel Diversity Coding

The Explicit Coding Rate Region of Symmetric Multilevel Diversity Coding

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