Conditions for Optimality of Superposition Coding in Discrete Memoryless Broadcast Channels

doi:10.1109/NCC.2019.8732209

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Conditions for Optimality of Superposition Coding in Discrete Memoryless Broadcast Channels

Proceedings Article•DOI•

Conditions for Optimality of Superposition Coding in Discrete Memoryless Broadcast Channels

Harikumar Krishnamurthy¹, Parikshit Hegde¹, Andrew Thangaraj¹•Institutions (1)

Indian Institute of Technology Madras¹

01 Feb 2019-pp 1-5

TL;DR: The results improve upon the previously known conditions for optimality of superposition coding in DMBCs and are shown to be optimal if and only if the two channels are more-capable comparable even without utput symmetry.

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Abstract: The capacity region of general discrete-memoryless broadcast channels (DMBCs) with two receivers is an open problem of considerable research interest. The optimality of superposition coding in three specific cases of the DMBC is considered. For a DMBC with binary input, symmetric output and output cardinality at most 3, superposition coding is shown to be optimal. For equal-capacity DMBCs with any input cardinality, superposition coding is shown to be suboptimal if each channel has a capacity-achieving input distribution that is not capacity-achieving for the other channel. For an equal-capacity DMBC with binary input, superposition coding is shown to be optimal if and only if the two channels are more-capable comparable even without utput symmetry. These results improve upon the previously known conditions for optimality of superposition coding in DMBCs.

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Book•

Elements of Information Theory (Wiley Series in Telecommunications and Signal Processing)

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Thomas M. Cover, Joy A. Thomas

01 Jul 2006

1,853 citations

"Conditions for Optimality of Superp..." refers background in this paper

...Consider a two-receiver, discrete memoryless broadcast channel [1] [2] with input X ∈ X resulting in outputs Yi ∈ Yi to Receiver i for i = 1, 2....
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Journal Article•DOI•

The capacity of a class of broadcast channels

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Abbas El Gamal

01 Mar 1979-IEEE Transactions on Information Theory

TL;DR: The capacity region is established for those discrete memoryless broadcast channels p(y,z \mid x) for which I(X;Y) \geq I (X;Z) holds for all Input distributions.

...read moreread less

Abstract: The capacity region is established for those discrete memoryless broadcast channels p(y,z \mid x) for which I(X;Y) \geq I(X;Z) holds for all Input distributions. The capacity region for this class of channels resembles the capacity region for degraded message sets considered by Korner and Marton.

...read moreread less

233 citations

"Conditions for Optimality of Superp..." refers background in this paper

...The superposition region is optimal if the two channels are either more-capable or e-lessnoisy comparable [12] [4]....
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...Since superposition coding is optimal if the two channels are more-capable or e-less noisy comparable [12] [4], the following corollary is immediate....
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Journal Article•DOI•

An Outer Bound to the Capacity Region of the Broadcast Channel

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Chandra Nair¹, A. El Gamal²•Institutions (2)

Microsoft¹, Stanford University²

01 Jan 2007-IEEE Transactions on Information Theory

TL;DR: An outer bound to the capacity region of the two-receiver discrete memoryless broadcast channel is given and is shown to be strict for the binary skew-symmetric broadcast channel.

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Abstract: An outer bound to the capacity region of the two-receiver discrete memoryless broadcast channel is given. The outer bound is tight for all cases where the capacity region is known. When specialized to the case of no common information, this outer bound is contained in the Koumlrner-Marton outer bound. This containment is shown to be strict for the binary skew-symmetric broadcast channel. Thus, this outer bound is in general tighter than all other known outer bounds.

...read moreread less

140 citations

"Conditions for Optimality of Superp..." refers background in this paper

...Characterising the capacity region in single letter (independent of n) is an open problem for general discretememoryless broadcast channels, and inner/outer bounds have been the topic of several recent papers [3]–[10]....
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Journal Article•DOI•

On a special class of broadcast channels with confidential messages

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M. van Dijk¹•Institutions (1)

Eindhoven University of Technology¹

01 Mar 1997-IEEE Transactions on Information Theory

TL;DR: It is shown that Csiszar and Korner's (1978) characterization of a discrete memoryless channel (DMC)X/spl rarr/Y as being less noisy than the DMC X/spl Rarr/Z is equivalent to the condition that the mutual-information difference I(X;Y)-I (X;Z) be a convex-/spl cap/ function of the probability distribution for X.

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Abstract: It is shown that Csiszar and Korner's (1978) characterization of a discrete memoryless channel (DMC)X/spl rarr/Y as being less noisy than the DMC X/spl rarr/Z is equivalent to the condition that the mutual-information difference I(X;Y)-I(X;Z) be a convex-/spl cap/ function of the probability distribution for X. This result is used to obtain a simple determination of the capacity region of the broadcast channel with confidential messages (BCC), which is a DMC X/spl rarr/(Y,Z), when the DMC X/spl rarr/Y to the legitimate receiver is less noisy than the DMC X/spl rarr/Z to the enemy cryptanalyst and there is a probability distribution for X having strictly positive components that achieves capacity on both these channels. In particular, when these DMC's are both symmetric, then the secrecy capacity of the BCC is the difference of their capacities. It is shown further that the less-noisy condition in this result cannot be weakened to the condition that the DMC X/spl rarr/Y be more capable than the DMC X/spl rarr/Z in the sense of Csiszar and Korner.

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121 citations

"Conditions for Optimality of Superp..." refers background in this paper

...Channel 1 is less noisy than Channel 2 if I1(x)− I2(x) is concave in [0, 1] [14]....
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Journal Article•DOI•

Capacity Regions of Two New Classes of Two-Receiver Broadcast Channels

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Chandra Nair¹•Institutions (1)

The Chinese University of Hong Kong¹

01 Sep 2010-IEEE Transactions on Information Theory

TL;DR: This work generalizes the notions of a less noisy receiver and a more capable receiver to an essentially less noisy Receiver and an essentially more capable Receiver, respectively, and establishes the capacity regions of these classes by borrowing on existing techniques.

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Abstract: Motivated by a simple broadcast channel, we generalize the notions of a less noisy receiver and a more capable receiver to an essentially less noisy receiver and an essentially more capable receiver, respectively. We establish the capacity regions of these classes by borrowing on existing techniques; however, these new classes contain additional interesting classes of broadcast channels, including the BSC/BEC broadcast channel. We also establish the relationships between the new classes and the existing classes.

...read moreread less

89 citations

"Conditions for Optimality of Superp..." refers background in this paper

...Note that (2) above is a sufficient condition for essentiallyless-noisy ordering introduced in [4] for the case of symmetric channels....
[...]
...Since superposition coding is optimal if the two channels are more-capable or e-less noisy comparable [12] [4], the following corollary is immediate....
[...]
...The superposition region is optimal if the two channels are either more-capable or e-lessnoisy comparable [12] [4]....
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