Nested Lattice Codes for Gaussian Relay Networks with Interference

In this paper, a class of relay networks is considered. We assume that, at a node, outgoing channels to its neighbors are orthogonal, while incoming signals from neighbors can interfere with each other. We are interested in the multicast capacity of these networks. As a subclass, we first focus on Gaussian relay networks with interference and find an achievable rate using a lattice coding scheme. It is shown that there is a constant gap between our achievable rate and the information theoretic cut-set bound. This is similar to the recent result by Avestimehr, Diggavi, and Tse, who showed such an approximate characterization of the capacity of general Gaussian relay networks. However, our achievability uses a structured code instead of a random one. Using the same idea used in the Gaussian case, we also consider linear finite-field symmetric networks with interference and characterize the capacity using a linear coding scheme.Comment: 23 pages, 5 figures, submitted to IEEE Transactions on Information Theor

Lattice Coding for the Two-way Two-relay Channel

Lattice coding techniques may be used to derive achievable rate regions which outperform known independent, identically distributed (i.i.d.) random codes in multi-source relay networks and in particular the two-way relay channel. Gains stem from the ability to decode the sum of codewords (or messages) using lattice codes at higher rates than possible with i.i.d. random codes. Here we develop a novel lattice coding scheme for the Two-way Two-relay Channel: 1 2 3 4, where Node 1 and 4 simultaneously communicate with each other through two relay nodes 2 and 3. Each node only communicates with its neighboring nodes. The key technical contribution is the lattice-based achievability strategy, where each relay is able to remove the noise while decoding the sum of several signals in a Block Markov strategy and then re-encode the signal into another lattice codeword using the so-called "Re-distribution Transform". This allows nodes further down the line to again decode sums of lattice codewords. This transform is central to improving the achievable rates, and ensures that the messages traveling in each of the two directions fully utilize the relay's power, even under asymmetric channel conditions. All decoders are lattice decoders and only a single nested lattice codebook pair is needed. The symmetric rate achieved by the proposed lattice coding scheme is within 0.5 log 3 bit/Hz/s of the symmetric rate capacity.Comment: submitted to IEEE Transactions on Information Theory on December 3, 201

A Novel User Pairing Scheme for Functional Decode-and-Forward Multi-way Relay Network

In this paper, we consider a functional decode and forward (FDF) multi-way relay network (MWRN) where a common user facilitates each user in the network to obtain messages from all other users. We propose a novel user pairing scheme, which is based on the principle of selecting a common user with the best average channel gain. This allows the user with the best channel conditions to contribute to the overall system performance. Assuming lattice code based transmissions, we derive upper bounds on the average common rate and the average sum rate with the proposed pairing scheme. Considering M-ary quadrature amplitude modulation with square constellation as a special case of lattice code transmission, we derive asymptotic average symbol error rate (SER) of the MWRN. We show that in terms of the achievable rates, the proposed pairing scheme outperforms the existing pairing schemes under a wide range of channel scenarios. The proposed pairing scheme also has lower average SER compared to existing schemes. We show that overall, the MWRN performance with the proposed pairing scheme is more robust, compared to existing pairing schemes, especially under worst case channel conditions when majority of users have poor average channel gains.Comment: 30 pages, 6 figures, submitted for journal publicatio

Lattice Codes for Many-to-One Interference Channels With and Without Cognitive Messages

A new achievable rate region is given for the Gaussian cognitive many-to-one interference channel. The proposed novel coding scheme is based on the compute-and-forward approach with lattice codes. Using the idea of decoding sums of codewords, our scheme improves considerably upon the conventional coding schemes which treat interference as noise or decode messages simultaneously. Our strategy also extends directly to the usual many-to-one interference channels without cognitive messages. Comparing to the usual compute-and-forward scheme where a fixed lattice is used for the code construction, the novel scheme employs scaled lattices and also encompasses key ingredients of the existing schemes for the cognitive interference channel. With this new component, our scheme achieves a larger rate region in general. For some symmetric channel settings, new constant gap or capacity results are established, which are independent of the number of users in the system.Comment: To appear in IEEE Transactions on Information Theor