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Cache-Aided Interference Management in Partially Connected Linear Networks

Fan Xu
Fan Xu
Tiankai Zheng
Tiankai Zheng

IEEE Transactions on Communications, pp. 301-316, 2020.

Cited by: 1|Bibtex|Views38|DOI:https://doi.org/10.1109/TCOMM.2019.2947438
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Other Links: dblp.uni-trier.de|academic.microsoft.com|arxiv.org
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We present a lower bound of the minimum normalized delivery time, followed by the discussion on the optimality of the achievable scheme presented in the previous sections

Abstract:

This paper studies caching in <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$(K\!+\!L\!-\!1)\!\times \!K$ </tex-math></inline-formula> partially connected wireless linear networks, where each of the <inline-formula xmlns:mml="http://www.w3.org/1998/...More

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Introduction
  • Caching is a novel solution to enhance the communication efficiency by exploiting the increasingly rich storage resource in wireless networks.
  • This is because the connected receiver set of transmitter j in the circular network, denoted as Rcj = {j − L + 1, j − L + 2, .
  • J} mod K, is the union of the connected receiver sets of transmitters j and K +j in the linear network, i.e., Rcj = Rj ∪ RK+j.
Highlights
  • Caching is a novel solution to enhance the communication efficiency by exploiting the increasingly rich storage resource in wireless networks
  • The authors in [4] showed that the original interference channel can be turned into more favorable channels including X channel and broadcast channel by proper file splitting and placement
  • We present a new file splitting and cache placement strategy, which is modified from the novel scheme in [8] by taking the partial network connectivity into account
  • Similar to Example 1, to ensure that each transmitter is connected to L receivers, we introduce virtual receivers to transform the network into the expanded partially connected linear interference networks
  • We present a lower bound of the minimum normalized delivery time, followed by the discussion on the optimality of the achievable scheme presented in the previous sections
  • The multiplicative gap between the achievable upper bound and the theoretical lower bound of the minimum normalized delivery time for the considered network is less than 2
Results
  • Each transmitter j has an encoding function Λj to map its cached content Uj, receiver demand d, and network-wide channel realization H = [hij (t)]i∈[K−1]+,j∈Ri,t∈[T ] to the signal (Xj[t])Tt=1 Λj(Uj, d, H), where T is the block length of the code.
  • The subfile Wn,1,{0,1}, which is cached in transmitters {1, 4} and receivers {0, 1, 3} in the 6 × 4 network in Fig. 1, has a size of a2F bits.
  • Note that transmitter 0 and 5 only have two coded messages to send, because the virtual receiver groups {−2, −1} and {4, 5} do not request any files.
  • The network topology is converted to an expanded partially connected Xmulticast channel with multicast size 2, where every set of two receivers form a multicast group, and desire a common message from any of the transmitters that are connected to both of them.
  • Denote vj{i1,i2} as the transmit beamforming vector of message Wt{ji1,i2} and Hij as the channel realization between transmitter j and receiver i.
  • Based on Algorithm 1, the network topology is converted into the expanded partially connected X-multicast channel with multicast size r + 1, where each transmitter j has an independent coded message WtRj intended to the actual receivers in multicast group R satisfying
  • (Achievable NDT) For the cache-aided (K + L − 1) × K partially connected linear interference network, an achievable NDT is given by the optimal solution of the following linear programming (LP) problem: τ ∗ ≤τub ar s.t.
Conclusion
  • The expression in (7) suggests that the proposed scheme III, the cached contents in the transmitter pair (j, K + j) of achieves the receiver local caching gain of (1 − μR) and the linear network will be identical when L is a divisor of a combined coded multicasting and transmitter coordination gain of
  • L − 1) × K partially connected linear interference network, the minimum NDT is lower-bounded by: APPENDIX A: PROOF OF LEMMA 1 τ ∗ ≥ 1 − μR.
  • Each transmitter j has an independent message, denoted as WtRj , aimed for the actual receivers in each of its connected receiver multicast group R satisfying
Summary
  • Caching is a novel solution to enhance the communication efficiency by exploiting the increasingly rich storage resource in wireless networks.
  • This is because the connected receiver set of transmitter j in the circular network, denoted as Rcj = {j − L + 1, j − L + 2, .
  • J} mod K, is the union of the connected receiver sets of transmitters j and K +j in the linear network, i.e., Rcj = Rj ∪ RK+j.
  • Each transmitter j has an encoding function Λj to map its cached content Uj, receiver demand d, and network-wide channel realization H = [hij (t)]i∈[K−1]+,j∈Ri,t∈[T ] to the signal (Xj[t])Tt=1 Λj(Uj, d, H), where T is the block length of the code.
  • The subfile Wn,1,{0,1}, which is cached in transmitters {1, 4} and receivers {0, 1, 3} in the 6 × 4 network in Fig. 1, has a size of a2F bits.
  • Note that transmitter 0 and 5 only have two coded messages to send, because the virtual receiver groups {−2, −1} and {4, 5} do not request any files.
  • The network topology is converted to an expanded partially connected Xmulticast channel with multicast size 2, where every set of two receivers form a multicast group, and desire a common message from any of the transmitters that are connected to both of them.
  • Denote vj{i1,i2} as the transmit beamforming vector of message Wt{ji1,i2} and Hij as the channel realization between transmitter j and receiver i.
  • Based on Algorithm 1, the network topology is converted into the expanded partially connected X-multicast channel with multicast size r + 1, where each transmitter j has an independent coded message WtRj intended to the actual receivers in multicast group R satisfying
  • (Achievable NDT) For the cache-aided (K + L − 1) × K partially connected linear interference network, an achievable NDT is given by the optimal solution of the following linear programming (LP) problem: τ ∗ ≤τub ar s.t.
  • The expression in (7) suggests that the proposed scheme III, the cached contents in the transmitter pair (j, K + j) of achieves the receiver local caching gain of (1 − μR) and the linear network will be identical when L is a divisor of a combined coded multicasting and transmitter coordination gain of
  • L − 1) × K partially connected linear interference network, the minimum NDT is lower-bounded by: APPENDIX A: PROOF OF LEMMA 1 τ ∗ ≥ 1 − μR.
  • Each transmitter j has an independent message, denoted as WtRj , aimed for the actual receivers in each of its connected receiver multicast group R satisfying
Tables
  • Table1: Subfiles to be delivered with r = |Q| = 1
Download tables as Excel
Funding
  • This work is supported by the National Natural Science Foundation of China under grants 61571299, 61329101, and 61521062
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