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Register a new userPrecoding and Scheduling for AoI Minimization in MIMO Broadcast Channels
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Added by
Songtao Feng
Publication date
2020
fields
Informatics Engineering
and research's language is
English
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In this paper, we consider a status updating system where updates are generated at a constant rate at $K$ sources and sent to the corresponding recipients through a broadcast channel. We assume that perfect channel state information (CSI) is available at the transmitter before each transmission, and the additive noise is negligible at the receivers. While the transmitter is able to utilize the CSI information to precode the updates, our object is to design optimal precoding schemes to minimize the summed average age of information (AoI) at the recipients. Under various assumptions on the size of each update and the number of antennas at the transmitter and the receivers, this paper identifies the corresponding age-optimal precoding and transmission scheduling strategies. Specifically, for the case where each user has one receiving antenna, a round-robin based updating scheme is shown to be optimal. For the two-user case where the number of antennas at each receiver is greater than the size of updates, a framed alternating updating scheme is proven to be optimal.
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Integer-forcing (IF) precoding, also known as downlink IF, is a promising new approach for communication over multiple-input multiple-output (MIMO) broadcast channels. Inspired by the integer-forcing linear receiver for multiple-access channels, it generalizes linear precoding by inducing an effective channel matrix that is approximately integer, rather than approximately identity. Combined with lattice encoding and a pre-inversion of the channel matrix at the transmitter, the scheme has the potential to outperform any linear precoding scheme, despite enjoying similar low complexity. In this paper, a specific IF precoding scheme, called diagonally-scaled exact IF (DIF), is proposed and shown to achieve maximum spatial multiplexing gain. For the special case of two receivers, in the high SNR regime, an optimal choice of parameters is derived analytically, leading to an almost closed-form expression for the achievable sum rate. In particular, it is shown that the gap to the sum capacity is upper bounded by 0.27 bits for any channel realization. For general SNR, a regularized version of DIF (RDIF) is proposed. Numerical results for two receivers under Rayleigh fading show that RDIF can achieve performance superior to optimal linear precoding and very close to the sum capacity.
Multiple-input multiple-output (MIMO) broadcast channels (BCs) (MIMO-BCs) with perfect channel state information (CSI) at the transmitter are considered. As joint user selection (US) and vector precoding (VP) (US-VP) with zero-forcing transmit beamforming (ZF-BF), US and continuous VP (CVP) (US-CVP) and data-dependent US (DD-US) are investigated. The replica method, developed in statistical physics, is used to analyze the energy penalties for the two US-VP schemes in the large-system limit, where the number of users, the number of selected users, and the number of transmit antennas tend to infinity with their ratios kept constant. Four observations are obtained in the large-system limit: First, the assumptions of replica symmetry (RS) and 1-step replica symmetry breaking (1RSB) for DD-US can provide acceptable approximations for low and moderate system loads, respectively. Secondly, DD-US outperforms CVP with random US in terms of the energy penalty for low-to-moderate system loads. Thirdly, the asymptotic energy penalty of DD-US is indistinguishable from that of US-CVP for low system loads. Finally, a greedy algorithm of DD-US proposed in authors previous work can achieve nearly optimal performance for low-to-moderate system loads.
Polar codes are introduced for discrete memoryless broadcast channels. For $m$-user deterministic broadcast channels, polarization is applied to map uniformly random message bits from $m$ independent messages to one codeword while satisfying broadcast constraints. The polarization-based codes achieve rates on the boundary of the private-message capacity region. For two-user noisy broadcast channels, polar implementations are presented for two information-theoretic schemes: i) Covers superposition codes; ii) Martons codes. Due to the structure of polarization, constraints on the auxiliary and channel-input distributions are identified to ensure proper alignment of polarization indices in the multi-user setting. The codes achieve rates on the capacity boundary of a few classes of broadcast channels (e.g., binary-input stochastically degraded). The complexity of encoding and decoding is $O(n*log n)$ where $n$ is the block length. In addition, polar code sequences obtain a stretched-exponential decay of $O(2^{-n^{beta}})$ of the average block error probability where $0 < beta < 0.5$.
A broadcast channel (BC) where the decoders cooperate via a one-sided link is considered. One common and two private messages are transmitted and the private message to the cooperative user should be kept secret from the cooperation-aided user. The secrecy level is measured in terms of strong secrecy, i.e., a vanishing information leakage. An inner bound on the capacity region is derived by using a channel-resolvability-based code that double-bins the codebook of the secret message, and by using a likelihood encoder to choose the transmitted codeword. The inner bound is shown to be tight for semi-deterministic and physically degraded BCs and the results are compared to those of the corresponding BCs without a secrecy constraint. Blackwell and Gaussian BC examples illustrate the impact of secrecy on the rate regions. Unlike the case without secrecy, where sharing information about both private messages via the cooperative link is optimal, our protocol conveys parts of the common and non-confidential messages only. This restriction reduces the transmission rates more than the usual rate loss due to secrecy requirements. An example that illustrates this loss is provided.
A partially cooperative relay broadcast channel (RBC) is a three-node network with one source node and two destination nodes (destinations 1 and 2) where destination 1 can act as a relay to assist destination 2. Inner and outer bounds on the capacity region of the discrete memoryless partially cooperative RBC are obtained. When the relay function is disabled, the inner and outer bounds reduce to new bounds on the capacity region of broadcast channels. Four classes of RBCs are studied in detail. For the partially cooperative RBC with degraded message sets, inner and outer bounds are obtained. For the semideterministic partially cooperative RBC and the orthogonal partially cooperative RBC, the capacity regions are established. For the parallel partially cooperative RBC with unmatched degraded subchannels, the capacity region is established for the case of degraded message sets. The capacity is also established when the source node has only a private message for destination 2, i.e., the channel reduces to a parallel relay channel with unmatched degraded subchannels.
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