Low Dimensional Lattice Codes For Bidirectional Relaying

We consider a communication system where two transmitters wish to exchange information through a central relay. The data is assumed to be transmitted over synchronized, average power constrained additive white Gaussian noise channels with a real input with signal-to-noise ratio (SNR) of snr. It has been shown that using lattice codes and lattice decoding, a rate of 1/2 log2 (1/2 + snr) can be obtained asymptotically, which is essentially optimal at high SNR. However, there has been a lack of practical encoding/decoding schemes for the above mentioned system. We address this issue in this thesis by developing encoding/decoding strategies for the bidirectional relaying system using low-dimensional lattice codes. Our efforts are aimed at developing coding schemes which possess low computational complexity while at the same time providing good performance. We demonstrate two schemes using low-dimensional lattice codes. Both these schemes have their own advantages and are suitable for different classes of lattice codes. The two schemes are tested with different lattices and their performance is compared to that of other schemes for bidirectional relays. The first scheme is termed as demodulate and forward and it essentially consists of performing optimal estimation at the relay. It is primarily implemented with lattice codes of low rate and possesses low decoding complexity. When used with a two-dimensional hexagonal lattice, it achieves a gain of around 3.5 dB in comparison to other schemes like Analog network coding. The second scheme is the sphere decoding scheme which has been implemented with high-rate lattice codes. The sphere decoder is a low-complexity decoder which is used for decoding to a lattice point at the relay. We observe that as the dimensionality of the lattice code is increased, the performance of the sphere decoder for the bidirectional relay gets consistently better. The sphere decoder is also used at high SNR for those instances in which the low density lattice code(LDLC) decoder makes an error and it is found that the sphere decoder can correct around 90 percent of these errors at an SNR of 9.75 dB.