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

An overview of Cu-based heterogeneous electrocatalysts for CO2 reduction

The electrochemical (EC) reduction of CO2 is a promising approach for value-added fuel or chemical production. Cu-based electrodes have been extensively used as a ‘star’ material for CO2 reduction to hydrocarbons. This review mainly focuses on the recent progress of Cu-based heterogeneous electrocatalysts for CO2 reduction from 2013 to 2019. Various morphologies of oxide-derived, bimetallic Cu species and their activity in EC CO2 reduction are reviewed, providing insights for the standardization of Cu-based heterogeneous systems. We also present a tutorial manual to describe parameters for the EC CO2 reduction process, especially for the pretreatment of the reaction system. This will offer useful guidance for newcomers to the field. Aqueous and non-aqueous electrolyte effects based on Cu electrodes are discussed. Finally, an overview of reaction systems of EC/PEC CO2 reduction and H2O oxidation for Cu-based heterogeneous catalysts is provided