Structured codes in network information theory
Song‐Nam Hong · University of Southern California Digital Library · 2014
Claude Shannon showed that unstructured random codes are shown to be optimal in many single user channels. In the past forty years, one of the major trusts of information theory has been extended this theory to the multi?terminal settings (known as network information theory). In this dissertation, we make progress on understanding the role of structured codes in several network settings. ? In the first part of this dissertation, we present a novel coding scheme nicknamed Reverse Compute and Forward for layered broadcast relay networks, where source wishes to transmit independent messages to the corresponding destinations with the aid of intermediate relays. This information theoretic model can capture the one of promising future wireless network architectures, known as cooperative distributed antenna systems or cloud radio access networks. In this scheme, each destination can reliably decode a linear combination of relays' messages (over suitable finite field), thanks to the algebraic structure of the proposed scheme. Then, the end?to?end interference over the finite field is completely eliminated by zero?forcing precoding (over finite field) at the source, namely, the decoded linear combination is nothing but the desired message of each destination. We show that our scheme is able to outperform the state of the art scheme called compressed dirty paper coding when the source?relay link capacity is limited. ? Next, we introduce a ""virtual"" full?duplex relay channel for which each relay stage in a multi?hop relaying network is formed by at least two relays, used alternatively in transmit and receive modes, such that while one relay transmits its signal to the next stage, the other relay receives a signal from the previous stage. With such a pipelined scheme, the source is active and sends a new information message in each time slot. For such channel, we show that structured code can almost achieve the upper bound when the channel gains have controlled fluctuations not larger than 3 dB, yielding a rate that does not depend on the number of relaying stages, while the rates of other schemes (based on random codes) degrade linearly or logarithmically with the number of stages. ? Finally, we study a number of two?user interference networks with multiple?antenna transmitters/receivers (MIMO), transmitter side information (cognition) in the form of linear combinations (over an appropriate finite field) of the information messages, and two?hop relaying. We show that in a cognitive Gaussian interference channel, if one node has a rank deficient linear combination of two messages, this can yield degrees of freedom and generalized degrees of freedom gains on the wireless segment, even though the coefficient of the linear combination are chosen at random and a priori (independent of the channel realization). This is the first time, as far as we know, that network coding in the wired part of the network is shown to yield DoFs gain on the wireless part of the network and shows that structured codes can be used jointly with other structured network coding techniques, such as linear network coding, even beyond the ""physical layer network coding"" ideas. Also, we characterize the symmetric sum rate of the two?user MIMO IC with coordination, cognition, and two?hops and provide finite signal?to?noise ratio results (not just degrees of freedom) which show that the proposed structured codes are competitive against state of the art interference avoidance based on orthogonal access, for standard randomly generated Rayleigh fading channels.