On the Capacity Regions of Degraded Relay Broadcast Channels with and without Feedback

The four-node relay broadcast channel (RBC) is considered, in which a transmitter communicates with two receivers with the assistance of a relay node. We first investigate three types of physically degraded RBCs (PDRBCs) based on different degradation orders among the relay and the receivers’ observed signals. For the discrete memoryless (DM) case, only the capacity region of the second type of PDRBC is already known, while for the Gaussian case, only the capacity region of the first type of PDRBC is already known. In this paper, we step forward and make the following progress: (1) for the first type of DM-PDRBC, a new outer bound is established, which has the same rate expression as an existing inner bound, with only a slight difference on the input distributions; (2) for the second type of Gaussian PDRBC, the capacity region is established; (3) for the third type of PDRBC, the capacity regions are established both for DM and Gaussian cases. Besides, we also consider the RBC with relay feedback where the relay node can send the feedback signal to the transmitter. A new coding scheme based on a hybrid relay strategy and a layered Marton’s coding is proposed. It is shown that our scheme can strictly enlarge Behboodi and Piantanida’s rate region, which is tight for the second type of DM-PDRBC. Moreover, we show that capacity regions of the second and third types of PDRBCs are exactly the same as that without feedback, which means feedback cannot enlarge capacity regions for these types of RBCs.

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An outer bound to the capacity region of broadcast channels (Corresp.)

IEEE Transactions on Information Theory ◽

10.1109/tit.1978.1055883 ◽

1978 ◽

Vol 24 (3) ◽

pp. 374-377 ◽

Cited By ~ 129

Author(s):

H. Sato

Keyword(s):

Broadcast Channels ◽

Capacity Region ◽

Outer Bound

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Compress-and-Forward for Relay Broadcast Channels without Common Messages

Cybernetics and Information Technologies ◽

10.1515/cait-2015-0031 ◽

2015 ◽

Vol 15 (2) ◽

pp. 97-110 ◽

Cited By ~ 1

Author(s):

Xiaoxia Song ◽

Yong Li

Keyword(s):

Relay Node ◽

Broadcast Channels ◽

Broadcast Channel ◽

Achievable Rate ◽

Decode And Forward ◽

Rate Region ◽

Gaussian Channels ◽

Memoryless Channels ◽

Peeling Off ◽

Better Than

Abstract This paper is connected with compress-and-forward strategy for two-user relay broadcast channels without common messages, where the relay node has private messages from the source, in addition to aiding traditional communication from the source to the destination. For this channel we derive two achievable rate regions based on the compress-and-forward strategy in cases of discrete memoryless channels and Gaussian channels, respectively. The numerical results for Gaussian relay broadcast channel show that the inner bound based on the compress-and-forward strategy improves when all the messages without peeling off any components are compressed and sent to the receiver. It also verifies that the inner bound based on compress-and-forward strategy is better than that based on decode-and-forward strategy, when the relay node is near to the sink node. Moreover, the rate region of the broadcast channel improves considerably when the collaboration between the two receivers is allowed. So the relay node can provide residual resources to help the communication between the source and the sink after its communication rate is satisfied, which gives some insights to select an available relay node in a practical communication system.

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MIMO Gaussian State-Dependent Channels with a State-Cognitive Helper

Entropy ◽

10.3390/e21030273 ◽

2019 ◽

Vol 21 (3) ◽

pp. 273 ◽

Cited By ~ 1

Author(s):

Michael Dikshtein ◽

Ruchen Duan ◽

Yingbin Liang ◽

Shlomo Shamai (Shitz)

Keyword(s):

Channel Coding ◽

The State ◽

Gaussian State ◽

Capacity Region ◽

Causal Knowledge ◽

Independent State ◽

Coding Scheme ◽

State Dependent ◽

Channel Parameters ◽

Outer Bound

We consider the problem of channel coding over multiterminal state-dependent channels in which neither transmitters nor receivers but only a helper node has a non-causal knowledge of the state. Such channel models arise in many emerging communication schemes. We start by investigating the parallel state-dependent channel with the same but differently scaled state corrupting the receivers. A cognitive helper knows the state in a non-causal manner and wishes to mitigate the interference that impacts the transmission between two transmit–receive pairs. Outer and inner bounds are derived. In our analysis, the channel parameters are partitioned into various cases, and segments on the capacity region boundary are characterized for each case. Furthermore, we show that for a particular set of channel parameters, the capacity region is entirely characterized. In the second part of this work, we address a similar scenario, but now each channel is corrupted by an independent state. We derive an inner bound using a coding scheme that integrates single-bin Gel’fand–Pinsker coding and Marton’s coding for the broadcast channel. We also derive an outer bound and further partition the channel parameters into several cases for which parts of the capacity region boundary are characterized.

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A Class of Three-Receiver Broadcast Channels with Degraded Message Sets and Side Information

Mathematical Problems in Engineering ◽

10.1155/2013/406826 ◽

2013 ◽

Vol 2013 ◽

pp. 1-8

Author(s):

Fangbiao Li ◽

Zhi Xue

Keyword(s):

Side Information ◽

Broadcast Channels ◽

Broadcast Channel ◽

Achievable Rate ◽

Secrecy Capacity ◽

Capacity Region ◽

Rate Region ◽

Special Cases ◽

Perfect Secrecy

We study a class of three-receiver discrete memoryless broadcast channel (DM-BC) with three degraded message sets and side information. We derive achievable rate region for this three-receive DM-BC with side information noncausally available at the transmitter. When the receivers follow a degradedness order, we determine the perfect secrecy capacity region of this class of three-receiver DM-BC with three degraded message sets and side information noncausally available at both the transmitter and the receiver. The achievable secrecy region of this paper subsumes Steinberg’s rate region for two-receiver degraded BC with the side information and the secrecy capacity region for one-receiver two-eavesdropper DM-BC with no side information as its special cases.

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Analysis of Side Information Impact on the Coverage Region of Wireless Wiretap Channel

10.21203/rs.3.rs-510207/v1 ◽

2021 ◽

Author(s):

saeid pakravan ◽

Ghosheh Abed Hodtani

Keyword(s):

Side Information ◽

Practical Importance ◽

Closed Form Expression ◽

Capacity Region ◽

Secrecy Rate ◽

Wiretap Channel ◽

Information Theoretic ◽

Rate Region ◽

Outer Bound ◽

Theoretical Results

Abstract Analyzing wireless communication performances by using information-theoretic results is of practical importance. In this paper, first, an achievable secrecy rate region and an outer bound on the secrecy capacity region for the discrete alphabet and memoryless wiretap channel with side information non-causally known at the transmitter are obtained. Then, by extending the results to the continuous alphabet wireless wiretap channel and by deriving a closed-form expression on the secrecy coverage region (SCR), as a remarkable wireless performance factor, impact of side information on the SCR is analyzed and it is shown that side information increases the SCR as expected intuitively. Numerical evaluation of theoretical results is done finally.

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