A Unified Relay Framework with both D-F and C-F Relay Nodes

Decode-and-forward (D-F) and compress-and-forward (C-F) are two fundamentally different relay strategies proposed by (Cover and El Gamal, 1979). Individually, either of them has been successfully generalized to multi-relay channels. In this paper, to allow each relay node the freedom of choosing either of the two strategies, we propose a unified framework, where both the D-F and C-F strategies can be employed simultaneously in the network. It turns out that, to fully incorporate the advantages of both the best known D-F and C-F strategies into a unified framework, the major challenge arises as follows: For the D-F relay nodes to fully utilize the help of the C-F relay nodes, decoding at the D-F relay nodes should not be conducted until all the blocks have been finished; However, in the multi-level D-F strategy, the upstream nodes have to decode prior to the downstream nodes in order to help, which makes simultaneous decoding at all the D-F relay nodes after all the blocks have been finished inapplicable. To tackle this problem, nested blocks combined with backward decoding are used in our framework, so that the D-F relay nodes at different levels can perform backward decoding at different frequencies. As such, the upstream D-F relay nodes can decode before the downstream D-F relay nodes, and the use of backward decoding at each D-F relay node ensures the full exploitation of the help of both the other D-F relay nodes and the C-F relay nodes. The achievable rates under our unified relay framework are found to combine both the best known D-F and C-F achievable rates and include them as special cases

Flow Decomposition for Multi-User Channels - Part I

A framework based on the idea of flow decomposition is proposed to characterize the decode-forward region for general multi-source, multi-relay, all-cast channels with independent input distributions. The region is difficult to characterize directly when deadlocks occur between two relay nodes, in which both relays benefit by decoding after each other. Rate-vectors in the decode-forward region depend ambiguously on the outcomes of all deadlocks in the channel. The region is characterized indirectly in two phases. The first phase assumes relays can operate non-causally. It is shown that every rate-vector in the decode-forward region corresponds to a set of flow decompositions, which describe the messages decoded at each node with respect to the messages forwarded by all the other nodes. The second phase imposes causal restrictions on the relays. Given an arbitrary set of (possibly non-causal) flow decompositions, necessary and sufficient conditions are derived for the existence of an equivalent set of causal flow decompositions that achieves the same rate-vector region

Federal Procurement and Equal Employment Opportunity

The paper contains a discussion about what results about the quality of an estimated model can be achieved, if no probabilitic assumptions are introduced. Several technical results that illustrate possibilities and difficulties are also given

A strong negative correlation between radio loudness RUVR_{\rm UV} and optical-to-X-ray spectral index αox\alpha_{\rm ox} in low-luminosity AGNs

It has been argued for years that the accretion mode changes from bright active galactic nuclei (AGNs) to low-luminosity AGNs (LLAGNs) at a rough dividing point of bolometric Eddington ratio $\lambda \sim 10^{-2}$. In this work, we strengthen this scenario through investigation of the relationship between the radio loudness $R_{\rm UV}$ and the optical-to-X-ray spectral index $\alpha_{\rm ox}$ in LLAGNs with $10^{-6} \lesssim \lambda \lesssim 10^{-3}$. We compile from literature a sample of 32 LLAGNs, consisting 18 LINERs and 14 low Eddington ratio Seyfert galaxies, and observe a strong negative $R_{\rm UV}$--$\alpha_{\rm ox}$ relationship, with large scatter in both $R_{\rm UV}$ and $\alpha_{\rm ox}$. We further demonstrate that this negative correlation, and the additional two negative relationships reported in literature ($R_{\rm UV}$--$\lambda$ and $\alpha_{\rm ox}$--$\lambda$ correlations), can be understood consistently and comprehensively under the truncated accretion--jet model, the model that has been applied successfully applied to LLAGNs. We argue that the scatter in the observations are (mainly) due to the spread in the viscosity parameter $\alpha$ of a hot accretion flow, a parameter that potentially can serve as a diagnose of the strength and/or configuration of magnetic fields in accretion flows.Comment: 8 pages, 3 figures, 2 tables. Accepted by MNRA