All achievable rate regions in  are based on ran- dom coding. In this paper, we use the lattice-based coding scheme (especially lattice alignment) to establish capac- ity regions for this channel. A comprehensive study on the performance of lattices is presented in . Perfor- mance of lattice codes over the additive white Gaussian noise (AWGN) channel is studied in . A dirty paper AWGN channel in which the interference is known non- causally or causally at the transmitter is investigated in . In , it is shown that the lattice coding strat- egy may outperform the DPC in a doubly dirty MAC. In , we also show that if the noise’s variance satisfies some constraints, then the capacity region of an addi- tive state-dependent Gaussianinterferencechannel with two independent channel states is achieved when the state power goes to infinity. In , a Gaussian relay channel with a state is considered in which the additive state is either added at the destination and known non-causally at the source or experienced at the relay and known at the destination. It is shown that a scheme based on nested lat- tice codes can achieve the capacity region within 0.5 bits. In , by using nested lattice codes, the generalized degrees of freedom for the two-user cognitive interferencechannel are characterized where one of the transmitters has knowledge of a linear combination of the two informa- tion messages. Using lattice codes for the state-dependent Gaussian Z-interferencechannel, some rate regions are established in .
Multiple Access-Cognitive InterferenceChannel (MA- CIFC) by merging a two-user MAC as a primary net- work and a cognitive transmitter-receiver pair in which the cognitive transmitter knows the message being sent by all of the transmitters in a non-causal manner. We analyzed the capacity region of MA-CIFC by deriving the inner and outer bounds on the capacity region of this channel. These bounds were proved to be tight in some special cases. Therefore, we determined the opti- mal strategy in these cases. Specifically, in the discrete memoryless case, we established the capacity regions for a class of degraded MA-CIFC and also under two sets of strong interference conditions. We also derive strong interference conditions for a network with k primary users. Further, we characterized the capacity region of the Gaussian MA-CIFC in the weak and strong interfer- ence regimes. We showed that DPC at the cognitive transmitter and treating interference as noise at the receivers, i.e., an oblivious primary receiver, are optimal in the weak interference. However, the receivers have to decode all messages when the interference is strong enough, which requires an aware primary receiver. Appendix A Proofs of Theorems 1, 2 and 3
V. P ROOFS
A. Auxiliary results
Before proceeding to the proof of Theorem 4 , we present the following non-asymptotic bounds on mutual information, which, in view of the alternative definition of information dimension in ( 10 ), implies the high-SNR scaling law of mutual information in Theorem 2 as an immediate corollary. This argument is considerably simpler and more general than the original result in [ 17 ]. This result also allows us to conclude that the capacity region of the interferencechannel ( 1 ) for non-Gaussian noise can differ only by absolute additive con- stants from the Gaussian counterpart if the noise has a well- behaved density such as uniform or Laplace distribution (see Remark 6 ).
Abstract--The technique to mitigate interference in the channel is very essential to maintain efficient signal transmission. Interference Alignment (IA) deals to mitigate interference and to enhance system efficiency of a wireless communication network. We deal with interference alignment scheme for a network with multiple cells and multiple multiple-input and multiple- output users under a Gaussianinterference broadcast channel scenario. At first we go for grouping method already known to a multiple-cells scenario and jointly design transmit and receiver beamforming vectors using a closed form expression without iterative computation. Then we go for a new approach using the principle of multiple access channel (MAC) - broadcast channel (BC) duality to perform interference alignment while maximizing capacity of users in each cell.
In this paper, we show that any complementary channel to the qubit depolarizing channel has positive quantum capacity (in fact, positive one-shot coherent information) unless the output is exactly constant. This is in sharp contrast with the superficially similar qubit depolarizing channel and erasure channel, whose capacities vanish when the analogous noise parameter is roughly half-way between the completely noiseless and noisy extremes. Prior to this work, it was not known (to our knowledge) that a family of quantum channels could retain positive quantum capacity while approaching a channel whose output is a fixed state, independent of the channel input. We hope this example concerning how the quantum capacity does not vanish will shed light on a better characterization of when a channel has no quantum capacity.
In this paper, we use the idea of quantum Graphic Cascade Coding, information theory security and quantum random coding theory to construct an immune noise channel by using the normal state of the pattern of tree chart and forest chart to make large diagonalzed matrices or blocks in order to performs quantum coding operations under multiple degrees of freedom. Through calculation and analysis of different concatenated code channelcapacity, we can get the formula of different noise channel in multi-channel coherence information under the coder multiple degrees of freedom. We can then quickly calculate the coherence information of various concatenated codes in the channel, the approximation of the channelcapacity and the noise margin of the channel transmission quantum, and analyzes the different anti-noise performance of different cascaded codes in different parameter channels, and obtains the security regions where different noise channels can transmit quantum information.
Several papers have been published regarding the capac- ity of SIMO systems operating in Nakagami environments. In , the channelcapacity of a SIMO system in a Nakagami- m fading channel is presented with the assumption that all links between transmit and receive antennas are independent and identically distributed (i.i.d.). In , capacity with MRC and optimal power and rate adaptation is presented while in  Shannon capacity with MRC is derived. In both of them, the assumption that all links are correlated and not identically distributed Nakagami holds. In , capacity of Nakagami-m multipath fading channels with MRC was studied for diﬀerent power and rate adaptation policies. Also, simple capacity formulas for correlated SIMO Nakagami-m channels were derived in . In , an analytical expression
Many other models for imprecise network information have been considered for interference networks. These models range from having no channel state information at the sources [10–13], delayed channel state information [14–19], mismatched delayed channel state knowledge [20–22], or analog channel state feedback for fully con- nected interference channels . Most of these works assume fully connected network or a small number of users. For networks with arbitrary connectivity, the first attempt to understand the role of limited network knowl- edge was initiated in [24, 25] in the context of single-layer networks. The authors used a message-passing abstrac- tion of network protocols to formalize the notion of local view. The key result of [24, 25] is that local-view-based (decentralized) decisions can be either sum rate optimal or can be arbitrarily worse than the global-view (central- ized) sum capacity. In this work, we focus on multi-layer setting and we show that several important additional ingredients are needed compared to the single-layer scenario.
The wiretap channel was introduced by Wyner in 1975 . The purpose of study wiretap channel is to maximize the rate of reliable communication from the source to the legitimate receiver, while the wiretapper learns as little as possible about the source output. Wyner has determined the achievable rate-equivocation region when both the main and the wiretap channels are discrete memoryless. Later Csiszár and Körner generalized Wyner’s wiretap channel , the model of which is depicted in Fig. 1. The capacity region of this model of wiretap channel was obtained in .
As shown by Shannon , having perfect knowledge about the channel, the Shannon capacity is achieved via updating the transmission power and rate relative to channel quality. However, assuming perfect channel information at the transmitter and receiver is an overly optimistic assumption, which does not match with reality [2–6]. Often, the receiver channel side information (CSI) is limited to knowledge of what SNR interval the channel quality belongs to, that is, the CSI is quantized to the best modulation and coding scheme (MCS) (see [3–6]). Then, implementing predefined coding and modulation selection tables, the transmitter is informed about the acceptable transmission rates via a limited number of feedback bits. This is a suboptimal but practical approach, and the considerable throughput improvement has led adaptive modulation with imperfect channel state information to be a major issue in, for example, the 3rd Generation Partnership Project (3GPP)  and some standards like UMTS/WCDMA .
In this paper we investigate various optimization techniques to achieve minimum area and cycle requirement. For the standard deviation 3.33, the most area-optimal implementation of the bit- scan operation based Knuth-Yao sampler consumes 30 slices on the Xilinx Virtex 5 FPGAs, and requires on average 17 cycles to generate a sample. We improve the speed of the sampler by using a precomputed table that directly maps the initial random bits into samples with very high probability. The fast sampler consumes 35 slices and spends on average 2.5 cycles to generate a sample. However the sampler architectures are not secure against timing and power analysis based attacks. In this paper we propose a random shuffle method to protect the Gaussian distributed polynomial against such attacks. The side channel attack resistant sampler architecture consumes 52 slices and spends on average 420 cycles to generate a polynomial of 256 coefficients.
We also evaluate the BER performance of compressive cooperation. Because the three DF schemes have very similar BER performance, we only present the results of code diversity scheme in Figure 5. The target rates of the ﬁve curves are computed at 6, 8, 10, 12, and 14 dB, respectively. For each target rate and its computed opti- mal parameters, we slightly vary the channel SNR and evaluate the average BER. An interesting ﬁnding from the ﬁgure is that the BER of compressive cooperation does not steeply increase when the channel condition decreases from the channel SNR that ensures reliable transmission. It is in sharp contrast to conventional coding and modu- lation schemes whose typical BER curves can be seen in Figure 6. This special BER property suggests that com- pressive transmission is more robust for highly dynamic channels where precise channel SNR is hard to obtain.
We use figure 2 as an example for analysis: First, the channel allocation starts from node a . Node b to node f is within the communication range of node a , so node a is assigned the same channel. When the sub-network centered on node a is expanding, it will select an appropriate node from the neighbors of node a for expansion. The selection criteria is to ensure that the expanded node has the largest number of unconnected neighbor nodes. As shown in the figure: Node d has the largest number of unconnected neighbors. So expand from node d . This can use the minimum resources to complete the basic connectivity of the network. And when expanding, it is possible to maximize the connectivity without disturbing the already formed subnets. Then the node that is about to expand selects a channel. To judge whether a channel can be allocated to a node, the following conditions must be met: The number of channels allocated to the node is smaller than the number of interfaces. And nodes that may cause interference do not use this channel.
Therefore, in this work, we develop a new algebraic methodology to quantize real-valued channels in order to realize interference alignment (IA)  onto a real ideal lattice and our channel model is given by equation (1). The coding scheme only requires that each relay knows the channel coefficients from each transmitter to itself.
A heterogeneous network example is illustrated in Figure 2.2. In such a configuration macro-cell eNodeBs belong to a Tier-1 network and femto-cell HeNodeBs belong to a Tier-2 network. Tier-1 network provides wide area coverage and serves large quantities of macro-cell UEs while tier-2 network serves indoor CSG users. One of the challenges that a heterogeneous network faces is the radio resource management between femto-cells and macro-cells. One could envision three interference management methods: exclusive frequency allocation, overlapping frequency allocation and partially overlapping frequency allocation, shown in Figure 2.3. Usually, radio frequency is used orthogonally, macro-cell and femto-cell each has an exclusive part. That, however, reduces the available capacity. It is more efficient to use whole spectrum in both macro-cell and femto-cells. If macro-cell and femto-cell use the same frequencies, they have to deal with the generated interference. The interference has to be maintained such that QoS target in all the cells remain within acceptable level. The inter-cell interference management and coordination are especially important for users at cell edge or overlapped area .
In this paper, the analytic expression for the ergodic chan- nel capacity or its lower bound of wireless communication systems with the Nakagami fading is presented for three spe- cial cases: (i) single transmit antenna and single receive an- tenna, (ii) single transmit and multiple receive antennas, and (iii) multiple transmit and single receive antennas, respec- tively. Formulae on the outage probability about the channelcapacity are also presented. Numerical results are provided to demonstrate the dependence of the channelcapacity on var- ious kinds of channel parameters. It is shown that increasing the number of receive antennas can obtain more benefit in channelcapacity than increasing the number of transmit an- tennas. Principally, the channelcapacity could be increased infinitely by employing a large number of receive antennas, but it appears to increase only logarithmically in this num- ber for SIMO case; while employing 3—5 transmit anten- nas can approach the best advantage of the multiple transmit antenna systems (irrespective of all other parameters consid- ered herein) as far as channelcapacity is concerned for MISO case. We have also observed that when the signal-to-noise ratio is low, the benefit in average capacity obtained by dis- tributing the available power to di ﬀ erent transmit antennas is very limited. We have shown numerically that for a given signal-to-noise ratio, the outage probability decreases consid- erably with the number of receive antennas for SIMO case, while for MISO case, the upper bound of the outage proba- bility decreases with the number of transmit antennas when the communication rate is lower than the critical transmis- sion rate ( R c ), but increases when the rate is higher than an-
The rapid development of communication systems with mobile receivers at higher data rates has lead to the importance of studies on information transfer over highly time varying channels. Under such circumstances, the channel variations become fast and the receiver is unable to track the channel during the predefined block length. Here existing results for the channelcapacity and the optimal input distri- bution, under the assumption of knowledge of the channel state information (CSI) are no longer valid. In reality the capacity is significantly reduced in the absence of the CSI at both the transmitter and the receiver. Furthermore, finding the optimal input distribution with no CSI is considered an important problem in information theory.
S-K mappings can be effectively designed for both bandwidth/dimension compression and expansion on point-to-point links [ 27 , 31 ]. Consider the dimension expansion of a single source (random variable): each source sample is mapped into M channel symbols or an M dimensional channel symbol. At the decoder side, the received noisy channel symbols are collected in M -tuples to jointly identify the single source sample. Such an expanding mapping, named 1:M mapping, can be realized by parametric curves residing in the channel space (as “continuous codebooks”), as shown in Figure 3 for the M = 2 and M = 3 case. The curves basically depict the one-dimensional source space as it appears in the channel space after being mapped through the S-K mapping. Noise will take the transmitted value away from the curve, and the task of the decoder is to identify the point on the curve that results in the smallest error. If we consider a Maximum Likelihood (ML) receiver, the decoded source symbol, ˆ x m , is the point on