Browsing by Subject "Physical Layer Network Coding"
Now showing 1 - 2 of 2
Results Per Page
Sort Options
Item Coding Schemes for Physical Layer Network Coding Over a Two-Way Relay Channel(2013-08-09) Hern, Brett MichaelWe consider a two-way relay channel in which two transmitters want to exchange information through a central relay. The relay observes a superposition of the trans- mitted signals from which a function of the transmitted messages is computed for broadcast. We consider the design of codebooks which permit the recovery of a function at the relay and derive information-theoretic bounds on the rates for reliable decoding at the relay. In the spirit of compute-and-forward, we present a multilevel coding scheme that permits reliable computation (or, decoding) of a class of functions at the relay. The function to be decoded is chosen at the relay depending on the channel realization. We define such a class of reliably computable functions for the proposed coding scheme and derive rates that are universally achievable over a set of channel gains when this class of functions is used at the relay. We develop our framework with general modulation formats in mind, but numerical results are presented for the case where each node transmits using 4-ary and 8-ary modulation schemes. Numerical results demonstrate that the flexibility afforded by our proposed scheme permits substantially higher rates than those achievable by always using a fixed function or considering only linear functions over higher order fields. Our numerical results indicate that it is favorable to allow the relay to attempt both compute-and-forward and decode-and-forward decoding. Indeed, either method considered separately is suboptimal for computation over general channels. However, we obtain a converse result when the transmitters are restricted to using identical binary linear codebooks generated uniformly at random. We show that it is impossible for this code ensemble to achieve any rate higher than the maximum of the rates achieved using compute-and-forward and decode-and-forward decoding. Finally, we turn our attention to the design of low density parity check (LDPC) ensembles which can practically achieve these information rates with joint-compute- and-forward message passing decoding. To this end, we construct a class of two-way erasure multiple access channels for which we can exactly characterize the performance of joint-compute-and-forward message passing decoding. We derive the processing rules and a density evolution like analysis for several classes of LDPC ensembles. Utilizing the universally optimal performance of spatially coupled LDPC ensembles with message passing decoding, we show that a single encoder and de- coder with puncturing can achieve the optimal rate region for a range of channel parameters.Item Parameter Estimation and Tracking in Physical Layer Network Coding(2012-07-16) Jain, ManishRecently, there has been a growing interest in improving the performance of the wireless relay networks through the use of Physical Layer Network Coding (PLNC) techniques. The physical layer network coding technique allows two terminals to transmit simultaneously to a relay node and decode the modulo-2 sum of the transmitted bits at the relay. This technique considerably improves performance over Digital Network Coding technique. In this thesis, we will present an algorithm for joint decoding of the modulo-2 sum of bits transmitted from two unsynchronized transmitters at the relay. We shall also address the problems that arise when boundaries of the signals do not align with each other and when the channel parameters are slowly varying and are unknown to the receiver at the relay node. Our approach will first jointly estimate the timing o sets and fading gains of both signals using a known pilot sequence sent by both transmitters in the beginning of the packet and then perform Maximum Likelihood detection of data using a state-based Viterbi decoding scheme that takes into account the timing o sets between the interfering signals. We shall present an algorithm for simultaneously tracking the amplitude and phase of slowly varying wireless channel that will work in conjunction our Maximum Likelihood detection algorithm. Finally, we shall provide extension of our receiver to support antenna diversity. Our results show that the proposed detection algorithm works reasonably well, even with the assumption of timing misalignment. We also demonstrate that the performance of the algorithm is not degraded by amplitude and/or phase mismatch between the users. We further show that the performance of the channel tracking algorithm is close to the ideal case i.e. when the channel estimates are perfectly known. Finally, we demonstrate the performance boost provided by the receiver antenna diversity.