Abstract-We present a distributed random linear network coding approach for transmission and compression of information in general multisource multicast networks. Network nodes independently and randomly select linear mappings from inputs onto output links over some field. We show that this achieves capacity with probability exponentially approaching 1 with the code length. We also demonstrate that random linear coding performs compression when necessary in a network, generalizing error exponents for linear Slepian-Wolf coding in a natural way. Benefits of this approach are decentralized operation and robustness to network changes or link failures. We show that this approach can take advantage of redundant network capacity for improved success probability and robustness. We illustrate some potential advantages of random linear network coding over routing in two examples of practical scenarios: distributed network operation and networks with dynamically varying connections. Our derivation of these results also yields a new bound on required field size for centralized network coding on general multicast networks.

Abstract-We study the maximum flow possible between a single-source and multiple terminals in a weighted random graph (modeling a wired network) and a weighted random geometric graph (modeling an ad-hoc wireless network) using network coding. For the weighted random graph model, we show that the network coding capacity concentrates around the expected number of nearest neighbors of the source and the terminals. Specifically, for a network with a single source, terminals, and relay nodes such that the link capacities between any two nodes is independent and identically distributed (i.i.d.), the maximum flow between the source and the terminals is approximately [ ] with high probability. For the weighted random geometric graph model where two nodes are connected if they are within a certain distance of each other we show that with high probability the network coding capacity is greater than or equal to the expected number of nearest neighbors of the node with the least coverage area.

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Abstract-Based on random codes and typical set decoding, an alternative proof of Root and Varaiya's compound channel coding theorem for linear Gaussian channels is presented. The performance limit of codes with finite block length under a compound channel is studied through error bounds and simulation. Although the theorem promises uniform convergence of the probability of error as the block length approaches infinity, with short block lengths the performance can differ considerably for individual channels. Simulation results show that universal performance can be a practical goal as the block lengths become large.Index Terms-Compound channel, random coding bound, sphere-packing bound (SPB), universal code.

We consider a multi-user MIMO downlink where the transmitter has only estimates of the channel while the receivers have perfect channel information. The impact of channel estimation error on the sum rate is studied. It is shown that the sum rate saturates due to the inaccurate channel information. In order to maintain full multiplexing gain, the channel estimation quality has to increase with at least the square root of data SNR but there is no need to increase more than linearly with the SNR. With user scheduling, the sum rate scales at least M/2 log log K, where K is the number of users and M is the number of transmit antennas. I. INTRODUCTIONMulti-user MIMO systems have attracted much interest from both academia and industry. By adding transmit antennas at the base station and using proper user scheduling algorithms, the sum rate of the downlink can be improved significantly. The improvement origins from two factors. The multiple transmit antennas create multiplexing gain and user scheduling creates multi-user diversity gain. The former is linear in the number of antennas [1], while the latter is double logarithmic in the number of users [2].One of the capacity-achieving schemes is the dirty paper coding (DPC) [3], which is very complex and hard to implement in practice. Suboptimal schemes like zero-forcing beamforming (ZFBF) [4] or MMSE beamforming [5] show impressive performance. The gain in sum rate however relies on the assumption that the transmitter has perfect channel side information (CSIT), a condition that is often unachievable in practical systems. On the other hand, the imperfect CSIT can take a severe toll on the sum rate capacity. For example, in [6] Lapidoth et. al. considered a system with two transmit antennas and two users each with single antenna. The authors showed that the sum rate capacity reduced by at least 1/3 due to the inaccuracy of the CSIT.The base station can multiplex pilots in the downlink data streams. The users may estimate the channel, quantize it and feed it back to the base. Alternatively, the base station can directly estimate the uplink channel through the pilots from the users. The former approach is applicable to both FDD and TDD systems but incurs extra feedback overhead. The latter approach, assuming channel reciprocity of the uplink and downlink, is only applicable to TDD systems and requires calibration between the two ends of the transmission. Although in both cases degradations in sum rate arises due to the imperfect CSIT, their causes are of different nature. The channel feedback approach has been extensively studied in [7],

In this paper, we propose a game-theoretical approach for energy-efficient resource allocation and interference coordination in heterogeneous networks (HetNets). Considering the joint interaction of cross-tier interference and energy consumption in a two-tier HetNet consisting of one central macro and N picos, we develop the system model and measure the energy efficiency (EE) by utility. Since global optimization of the HetNet EE is intractable and computationally expensive, we formulate the optimization problems for macro and picos respectively as a two-stage Stackelberg game. Then we employ a backward induction method to solve this game model and analyze the method complexity. Simulation results verify the performance of the proposed approach and it can be easily implemented in a distributed manner in practical HetNets.

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