Achieving the Uniform Rate Region of General Multiple Access Channels by Polar Coding

We consider the problem of polar coding for transmission over $m$-user multiple access channels. In the proposed scheme, all users encode their messages using a polar encoder, while a multi-user successive cancellation decoder is deployed at the receiver. The encoding is done separately across the users and is independent of the target achievable rate. For the code construction, the positions of information bits and frozen bits for each of the users are decided jointly. This is done by treating the polar transformations across all the $m$ users as a single polar transformation with a certain \emph{polarization base}. We characterize the resolution of achievable rates on the dominant face of the uniform rate region in terms of the number of users $m$ and the length of the polarization base $L$. In particular, we prove that for any target rate on the dominant face, there exists an achievable rate, also on the dominant face, within the distance at most $\frac{(m-1)\sqrt{m}}{L}$ from the target rate. We then prove that the proposed MAC polar coding scheme achieves the whole uniform rate region with fine enough resolution by changing the decoding order in the multi-user successive cancellation decoder, as $L$ and the code block length $N$ grow large. The encoding and decoding complexities are $O(N \log N)$ and the asymptotic block error probability of $O(2^{-N^{0.5 - \epsilon}})$ is guaranteed. Examples of achievable rates for the $3$-user multiple access channel are provided

A Survey of Physical Layer Security Techniques for 5G Wireless Networks and Challenges Ahead

Physical layer security which safeguards data confidentiality based on the information-theoretic approaches has received significant research interest recently. The key idea behind physical layer security is to utilize the intrinsic randomness of the transmission channel to guarantee the security in physical layer. The evolution towards 5G wireless communications poses new challenges for physical layer security research. This paper provides a latest survey of the physical layer security research on various promising 5G technologies, including physical layer security coding, massive multiple-input multiple-output, millimeter wave communications, heterogeneous networks, non-orthogonal multiple access, full duplex technology, etc. Technical challenges which remain unresolved at the time of writing are summarized and the future trends of physical layer security in 5G and beyond are discussed.Comment: To appear in IEEE Journal on Selected Areas in Communication

On the Capacity Region of Multi-Antenna Gaussian Broadcast Channels with Estimation Error

In this paper we consider the effect of channel estimation error on the capacity region of MIMO Gaussian broadcast channels. It is assumed that the receivers and the transmitter have (the same) estimates of the channel coefficients (i.e., the feedback channel is noiseless). We obtain an achievable rate region based on the dirty paper coding scheme. We show that this region is given by the capacity region of a dual multi-access channel with a noise covariance that depends on the transmit power. We explore this duality to give the asymptotic behavior of the sum-rate for a system with a large number of user, i.e., n rarr infin. It is shown that as long as the estimation error is of fixed (w.r.t n) variance, the sum-capacity is of order M log log n, where M is the number of antennas deployed at the transmitter. We further obtain the sum-rate loss due to the estimation error. Finally, we consider a training-based scheme for block fading MISO Gaussian broadcast channels. We find the optimum length of the training interval as well as the optimum power used for training in order to maximize the achievable sum-rate

Weak Secrecy in the Multi-Way Untrusted Relay Channel with Compute-and-Forward

We investigate the problem of secure communications in a Gaussian multi-way relay channel applying the compute-and-forward scheme using nested lattice codes. All nodes employ half-duplex operation and can exchange confidential messages only via an untrusted relay. The relay is assumed to be honest but curious, i.e., an eavesdropper that conforms to the system rules and applies the intended relaying scheme. We start with the general case of the single-input multiple-output (SIMO) L-user multi-way relay channel and provide an achievable secrecy rate region under a weak secrecy criterion. We show that the securely achievable sum rate is equivalent to the difference between the computation rate and the multiple access channel (MAC) capacity. Particularly, we show that all nodes must encode their messages such that the common computation rate tuple falls outside the MAC capacity region of the relay. We provide results for the single-input single-output (SISO) and the multiple-input single-input (MISO) L-user multi-way relay channel as well as the two-way relay channel. We discuss these results and show the dependency between channel realization and achievable secrecy rate. We further compare our result to available results in the literature for different schemes and show that the proposed scheme operates close to the compute-and-forward rate without secrecy.Comment: submitted to JSAC Special Issue on Fundamental Approaches to Network Coding in Wireless Communication System