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We investigate the performance of multi-level polar coded modulation in the decode-forward relay channel. We begin by numerically analyzing the rates assigned to polar codes of all levels via chain rule and error exponent. The construction of polar codes follows the 5G standard. A joint decoding based on maximum ratio combining with multistage decoding is proposed for the destination. We simulate the error performance under 16QAM with gray labeling and Ungerboeck's set partitioning. In the half-duplex mode, a gain of 2.5dB is observed compared with the state of the art, consisting of 0.7 dB gain due to multistage decoding and 1.8dB gain due to the choice of labeling. In addition, the error performance according to error exponent is compared with the chain rule. A dispersion bound for the decode-forward relaying is calculated. 

Abstract Recent progress in the understanding of the behavior of the interference channel has led to valuable insights: first, discrete signaling has been discovered to have tangible benefits in the presence of interference, especially when one does not wish to decode the interfering signal, i.e., the interference is treated as noise, and second, the capacity of the interference channel as a function of the interference link gains is now understood to be highly irregular, i.e., non-monotonic and discontinuous. This work addresses these two issues in an integrated and interdisciplinary manner: it utilizes discrete signaling to approach the capacity of the interference channel by developing lower bounds on the mutual information under discrete modulation and treating interference as noise, subject to an outage set, and addresses the issue of sensitivity to link gains with a liquid metal reconfigurable antenna to avoid the aforementioned outage sets. Simulations illustrate the effectiveness of our approach. 

Community detection refers to recovering a (latent) label on which the distribution of the observed graph depends. Recent work has also investigated the impact of additionally knowing the value of another variable at each vertex that is correlated with the vertex label (side information), while assuming side information is independent of the graph edges conditioned on the label. This work extends the scope of community detection in two ways. First, we consider a side information that does not form a Markov chain with the label and graph, and analyze the detection threshold of semidefinite programming subject to knowledge of this side information, which is a non-label latent variable on which the graph edges also depend. In the second part of the work, we consider aside from vertex labels a second latent variable that is unknown both in realization and in distribution. We then investigate the performance of the semidefinite programming community detection as a function of the (unknown) composition of the nuisance latent variable. In both cases, it is shown that semidefinite programming can achieve exact recovery down to the optimal (information theoretic) threshold. 

We investigate the performance of discrete (coded) modulations in the full-duplex compress-forward relay channel using multilevel coding. We numerically analyze the rates assigned to component binary codes of all levels. LDPC codes are used as the component binary codes to provide error protection. The compression at the relay is done via a nested scalar quantizer whose output is mapped to a codeword through LDPC codes. A compound Tanner graphical model and information-exchange algorithm are described for joint decoding of both messages sent from the source and relay. Simulation results show that the performance of the proposed system based on multilevel coding is better than that based on BICM, and is separated from the SNR threshold of the known CF achievable rate by two factors consisting approximately of the sum of the shaping gain (due to scalar quantization) and the separation of the LDPC code implementation from AWGN capacity.