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Register a new userThe Capacity on Degraded Relay Broadcast Channel
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Added by
Youlong Wu
Publication date
2018
fields
Informatics Engineering
and research's language is
English
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The relay broadcast channel (RBC) is considered, in which a transmitter communicates with two receivers with the assistance of a relay. Based on different degradation orders among the relay and the receivers outputs, three types of physically degraded RBCs (PDRBCs) are introduced. Inner bounds and outer bounds are derived on the capacity region of the presented three types. The bounds are tight for two types of PDRBCs: 1) one receivers output is a degraded form of the other receivers output, and the relays output is a degraded form of the weaker receivers output; 2) one receivers output is a degraded form of the relays output, and the other receivers output is a degraded form of the relays output. For the Gaussian PDRBC, the bounds match, i.e., establish its capacity region.
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Degraded K-user broadcast channels (BC) are studied when receivers are facilitated with cache memories. Lower and upper bounds are derived on the capacity-memory tradeoff, i.e., on the largest rate of reliable communication over the BC as a function of the receivers cache sizes, and the bounds are shown to match for some special cases. The lower bounds are achieved by two new coding schemes that benefit from non-uniform cache assignment. Lower and upper bounds are also established on the global capacity-memory tradeoff, i.e., on the largest capacity-memory tradeoff that can be attained by optimizing the receivers cache sizes subject to a total cache memory budget. The bounds coincide when the total cache memory budget is sufficiently small or sufficiently large, characterized in terms of the BC statistics. For small cache memories, it is optimal to assign all the cache memory to the weakest receiver. In this regime, the global capacity-memory tradeoff grows as the total cache memory budget divided by the number of files in the system. In other words, a perfect global caching gain is achievable in this regime and the performance corresponds to a system where all cache contents in the network are available to all receivers. For large cache memories, it is optimal to assign a positive cache memory to every receiver such that the weaker receivers are assigned larger cache memories compared to the stronger receivers. In this regime, the growth rate of the global capacity-memory tradeoff is further divided by the number of users, which corresponds to a local caching gain. Numerical indicate suggest that a uniform cache-assignment of the total cache memory is suboptimal in all regimes unless the BC is completely symmetric. For erasure BCs, this claim is proved analytically in the regime of small cache-sizes.
In this paper, the capacity region of the Layered Packet Erasure Broadcast Channel (LPE-BC) with Channel Output Feedback (COF) available at the transmitter is investigated. The LPE-BC is a high-SNR approximation of the fading Gaussian BC recently proposed by Tse and Yates, who characterized the capacity region for any number of users and any number of layers when there is no COF. This paper derives capacity inner and outer bounds for the LPE-BC with COF for the case of two users and any number of layers. The inner bounds generalize past results for the two-user erasure BC, which is a special case of the LPE-BC with COF with only one layer. The novelty lies in the use of emph{inter-user & inter-layer network coding} retransmissions (for those packets that have only been received by the unintended user), where each random linear combination may involve packets intended for any user originally sent on any of the layers. Analytical and numerical examples show that the proposed outer bound is optimal for some LPE-BCs.
The capacity regions are investigated for two relay broadcast channels (RBCs), where relay links are incorporated into standard two-user broadcast channels to support user cooperation. In the first channel, the Partially Cooperative Relay Broadcast Channel, only one user in the system can act as a relay and transmit to the other user through a relay link. An achievable rate region is derived based on the relay using the decode-and-forward scheme. An outer bound on the capacity region is derived and is shown to be tighter than the cut-set bound. For the special case where the Partially Cooperative RBC is degraded, the achievable rate region is shown to be tight and provides the capacity region. Gaussian Partially Cooperative RBCs and Partially Cooperative RBCs with feedback are further studied. In the second channel model being studied in the paper, the Fully Cooperative Relay Broadcast Channel, both users can act as relay nodes and transmit to each other through relay links. This is a more general model than the Partially Cooperative RBC. All the results for Partially Cooperative RBCs are correspondingly generalized to the Fully Cooperative RBCs. It is further shown that the AWGN Fully Cooperative RBC has a larger achievable rate region than the AWGN Partially Cooperative RBC. The results illustrate that relaying and user cooperation are powerful techniques in improving the capacity of broadcast channels.
Capacity gains from transmitter and receiver cooperation are compared in a relay network where the cooperating nodes are close together. Under quasi-static phase fading, when all nodes have equal average transmit power along with full channel state information (CSI), it is shown that transmitter cooperation outperforms receiver cooperation, whereas the opposite is true when power is optimally allocated among the cooperating nodes but only CSI at the receiver (CSIR) is available. When the nodes have equal power with CSIR only, cooperative schemes are shown to offer no capacity improvement over non-cooperation under the same network power constraint. When the system is under optimal power allocation with full CSI, the decode-and-forward transmitter cooperation rate is close to its cut-set capacity upper bound, and outperforms compress-and-forward receiver cooperation. Under fast Rayleigh fading in the high SNR regime, similar conclusions follow. Cooperative systems provide resilience to fading in channel magnitudes; however, capacity becomes more sensitive to power allocation, and the cooperating nodes need to be closer together for the decode-and-forward scheme to be capacity-achieving. Moreover, to realize capacity improvement, full CSI is necessary in transmitter cooperation, while in receiver cooperation optimal power allocation is essential.
A class of diamond networks is studied where the broadcast component is orthogonal and modeled by two independent bit-pipes. New upper and lower bounds on the capacity are derived. The proof technique for the upper bound generalizes bounding techniques of Ozarow for the Gaussian multiple description problem (1981) and Kang and Liu for the Gaussian diamond network (2011). The lower bound is based on Martons coding technique and superposition coding. The bounds are evaluated for Gaussian and binary adder multiple access channels (MACs). For Gaussian MACs, both the lower and upper bounds strengthen the Kang-Liu bounds and establish capacity for interesting ranges of bit-pipe capacities. For binary adder MACs, the capacity is established for all ranges of bit-pipe capacities.
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