Jingge Zhu

Gaussian (dirty) multiple access channels: a compute-and-forward perspective

Lattice codes are applied to the two-user Gaussian multiple access channel (MAC) combined with a modified compute-and-forward transmitting scheme. It is shown that non-corner points on the boundary of the capacity region can be achieved by decoding two integer sums of the codewords, which can be viewed as a generalization of the well-known successive cancellation decoding. A similar idea is then applied to the so-called dirty MAC where two interfering signals are known non-causally to the two transmitters in a distributed fashion. Our scheme recovers previously known results and gives new achievable rate regions. The proposed scheme can be extended to the case with more than two users.

Typical sumsets of linear codes

Given two identical linear codes C with rate R over Fq of length n, we independently pick one codeword from each codebook uniformly at random. A sumset is formed by adding these two codewords entry-wise as integer vectors and a sumset is called typical, if the sum falls inside this set with high probability. In this paper we show that the asymptotic size of such typical sumsets for most codes is min{22nR, 2n(R+D)} where D depends solely on the alphabet size q. More generally, we completely characterize the asymptotic size of typical sumsets of two nested linear codes C1, C2 with different rates. We also provide two applications of the results, one on a computation problem over the general two-user multiple-access channel, and one on a communication problem over an additive two-user multiple-access channel.

On lattice codes for Gaussian interference channels

The usefulness of lattice codes is investigated for two-user Gaussian interference channels (IC). A coding scheme based on the compute-and-forward technique is shown to achieve the capacity region of the Gaussian IC under strong interference. The proposed scheme uses single-user decoders whereas the conventional scheme uses multi-user decoders for simultaneous decoding. The same scheme is applicable to the Gaussian Z-interference channel. A lattice-based coding scheme is also devised for the state-dependent Gaussian IC with the state sequence non-causally known to transmitters. The proposed scheme establishes new achievable rate regions, which can be considerably larger than the best known results, especially when the interfering state sequence has very large power.

Compute-and-forward using nested linear codes for the Gaussian MAC

The classical modulo-lattice construction of Erez et al. has been successfully applied to several coding problems under Gaussian noise, including coding for computation over multiple-access channels (MAC). For the latter problem, an alternative construction can be developed by extending a recently proposed nested linear code to Gaussian case. In this note, it is shown that using the nested linear code with judiciously chosen input distributions, the original compute-and-forward result is recovered and larger computation rates are achievable. In particular we show that the Gaussian input distribution is not optimal in general for the computation problem over Gaussian MAC. Among other results, new achievable rates for the Gaussian two-way relay channel (TWRC) are given.

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.

Lattice codes for many-to-one cognitive interference networks

In this work we consider the cognitive many-to-one interference network. We first extend existing coding schemes from the two-user case to this network scenario. Then we present a novel coding scheme using compute-and-forward and show it can enlarge the achievable rate region considerably for a wide range of parameters. Numerical evaluations are given to compare the performance of different schemes. Specializing the results to symmetric settings, for a range of parameters, our achievable rate region is shown to be within a constant gap from capacity, regardless of the number of cognitive users.