Wireless Network Information Flow: A Deterministic Approach

In a wireless network with a single source and a single destination and an arbitrary number of relay nodes, what is the maximum rate of information flow achievable? We make progress on this long standing problem through a two-step approach. First we propose a deterministic channel model which captures the key wireless properties of signal strength, broadcast and superposition. We obtain an exact characterization of the capacity of a network with nodes connected by such deterministic channels. This result is a natural generalization of the celebrated max-flow min-cut theorem for wired networks. Second, we use the insights obtained from the deterministic analysis to design a new quantize-map-and-forward scheme for Gaussian networks. In this scheme, each relay quantizes the received signal at the noise level and maps it to a random Gaussian codeword for forwarding, and the final destination decodes the source's message based on the received signal. We show that, in contrast to existing schemes, this scheme can achieve the cut-set upper bound to within a gap which is independent of the channel parameters. In the case of the relay channel with a single relay as well as the two-relay Gaussian diamond network, the gap is 1 bit/s/Hz. Moreover, the scheme is universal in the sense that the relays need no knowledge of the values of the channel parameters to (approximately) achieve the rate supportable by the network. We also present extensions of the results to multicast networks, half-duplex networks and ergodic networks.Comment: To appear in IEEE transactions on Information Theory, Vol 57, No 4, April 201

Distortion Minimization in Gaussian Layered Broadcast Coding with Successive Refinement

A transmitter without channel state information (CSI) wishes to send a delay-limited Gaussian source over a slowly fading channel. The source is coded in superimposed layers, with each layer successively refining the description in the previous one. The receiver decodes the layers that are supported by the channel realization and reconstructs the source up to a distortion. The expected distortion is minimized by optimally allocating the transmit power among the source layers. For two source layers, the allocation is optimal when power is first assigned to the higher layer up to a power ceiling that depends only on the channel fading distribution; all remaining power, if any, is allocated to the lower layer. For convex distortion cost functions with convex constraints, the minimization is formulated as a convex optimization problem. In the limit of a continuum of infinite layers, the minimum expected distortion is given by the solution to a set of linear differential equations in terms of the density of the fading distribution. As the bandwidth ratio b (channel uses per source symbol) tends to zero, the power distribution that minimizes expected distortion converges to the one that maximizes expected capacity. While expected distortion can be improved by acquiring CSI at the transmitter (CSIT) or by increasing diversity from the realization of independent fading paths, at high SNR the performance benefit from diversity exceeds that from CSIT, especially when b is large.Comment: Accepted for publication in IEEE Transactions on Information Theor

On the Non-Orthogonal Layered Broadcast Codes in Cooperative Wireless Networks

A multi-fold increase in spectral efficiency and throughput are envisioned in the fifth generation of cellular networks to meet the requirements of International Telecommunication Union (ITU) IMT-2020 on massive connectivity and tremendous data traffic. This is achieved by evolution in three aspects of current networks. The first aspect is shrinking the cell sizes and deploying dense picocells and femtocells to boost the spectral reuse. The second is to allocate more spectrum resources including millimeter-wave bands. The third is deploying highly efficient communications and multiple access techniques. Non-orthogonal multiple access (NOMA) is a promising communication technique that complements the current commercial spectrum access approach to boost the spectral efficiency, where different data streams/users’ data share the same time, frequency and code resource blocks (sub-bands) via superimposition with each other. The receivers decode their own messages by deploying the successive interference cancellation (SIC) decoding rule. It is known that the NOMA coding is superior to conventional orthogonal multiple access (OMA) coding, where the resources are split among the users in either time or frequency domain. The NOMA based coding has been incorporated into other coding techniques including multi-input multi-output (MIMO), orthogonal frequency division multiplexing (OFDM), cognitive radio and cooperative techniques. In cooperative NOMA codes, either dedicated relay stations or stronger users with better channel conditions, act as relay to leverage the spatial diversity and to boost the performance of the other users. The advantage of spatial diversity gain in relay-based NOMA codes, is deployed to extend the coverage area of the network, to mitigate the fading effect of multipath channel and to increase the system throughput, hence improving the system efficiency. In this dissertation we consider the multimedia content delivery and machine type communications over 5G networks, where scalable content and low complexity encoders is of interest. We propose cross-layer design for transmission of successive refinement (SR) source code interplayed with non-orthogonal layered broadcast code for deployment in several cooperative network architectures. Firstly, we consider a multi-relay coding scheme where a source node is assisted by a half-duplex multi-relay non-orthogonal amplify-forward (NAF) network to communicate with a destination node. Assuming the channel state information (CSI) is not available at the source node, the achievable layered diversity multiplexing tradeoff (DMT) curve is derived. Then, by taking distortion exponent (DE) as the figure of merit, several achievable lower bounds are proved, and the optimal expected distortion performance under high signal to noise ratio (SNR) approximation is explicitly obtained. It is shown that the proposed coding can achieve the multi-input single-output (MISO) upper bound under certain regions of bandwidth ratios, by which the optimal performance in these regions can be explicitly characterized. Further the non-orthogonal layered coding scheme is extended to a multi-hop MIMO decode-forward (DF) relay network where a set of DE lower bounds is derived. Secondly, we propose a layered cooperative multi-user scheme based on non-orthogonal amplify-forward (NAF) relaying and non-orthogonal multiple access (NOMA) codes, aiming to achieve multi-user uplink transmissions with low complexity and low signaling overhead, particularly applicable to the machine type communications (MTC) and internet of things (IoT) systems. By assuming no CSI available at the transmitting nodes, the proposed layered codes make the transmission rate of each user adaptive to the channel realization. We derive the close-form analytical results on outage probability and the DMT curve of the proposed layered NAF codes in the asymptotic regime of high SNR, and optimize the end-to-end performance in terms of the exponential decay rate of expected distortion. Thirdly, we consider a single relay network and study the non-orthogonal layered scheme in the general SNR regime. A layered relaying scheme based on compress-forward (CF) is introduced, where optimization of end to end performance in terms of expected distortion is conducted to jointly determine network parameters. We further derive the explicit analytical optimal solution with two layers in the absence of channel knowledge. Finally, we consider the problem of multicast of multi-resolution layered messages over downlink of a cellular system with the assumption of CSI is not available at the base station (BS). Without loss generality, spatially random users are divided into two groups, where the near group users with better channel conditions decode for both layers, while the users in the second group decode for base layer only. Once the BS launches a multicast message, the first group users who successfully decoded the message, deploy a distributed cooperating scheme to assist the transmission to the other users. The cooperative scheme is naive but we will prove it can effectively enhance the network capacity. Closed form outage probability is explicitly derived for the two groups of users. Further it is shown that diversity order equal to the number of users in the near group is achievable, hence the coding gain of the proposed distributed scheme fully compensate the lack of CSI at the BS in terms of diversity order

Minimum Expected Distortion in Gaussian Layered Broadcast Coding with Successive Refinement

A transmitter without channel state information (CSI) wishes to send a delay-limited Gaussian source over a slowly fading channel. The source is coded in superimposed layers, with each layer successively refining the description in the previous one. The receiver decodes the layers that are supported by the channel realization and reconstructs the source up to a distortion. In the limit of a continuum of infinite layers, the optimal power distribution that minimizes the expected distortion is given by the solution to a set of linear differential equations in terms of the density of the fading distribution. In the optimal power distribution, as SNR increases, the allocation over the higher layers remains unchanged; rather the extra power is allocated towards the lower layers. On the other hand, as the bandwidth ratio b (channel uses per source symbol) tends to zero, the power distribution that minimizes expected distortion converges to the power distribution that maximizes expected capacity. While expected distortion can be improved by acquiring CSI at the transmitter (CSIT) or by increasing diversity from the realization of independent fading paths, at high SNR the performance benefit from diversity exceeds that from CSIT, especially when b is large.Comment: To appear in the proceedings of the 2007 IEEE International Symposium on Information Theory, Nice, France, June 24-29, 200

Joint Source-Channel Codes for MIMO Block Fading Channels

We consider transmission of a continuous amplitude source over an L-block Rayleigh fading $M_t \times M_r$ MIMO channel when the channel state information is only available at the receiver. Since the channel is not ergodic, Shannon's source-channel separation theorem becomes obsolete and the optimal performance requires a joint source -channel approach. Our goal is to minimize the expected end-to-end distortion, particularly in the high SNR regime. The figure of merit is the distortion exponent, defined as the exponential decay rate of the expected distortion with increasing SNR. We provide an upper bound and lower bounds for the distortion exponent with respect to the bandwidth ratio among the channel and source bandwidths. For the lower bounds, we analyze three different strategies based on layered source coding concatenated with progressive, superposition or hybrid digital/analog transmission. In each case, by adjusting the system parameters we optimize the distortion exponent as a function of the bandwidth ratio. We prove that the distortion exponent upper bound can be achieved when the channel has only one degree of freedom, that is L=1, and $\min\{M_t,M_r\}=1$. When we have more degrees of freedom, our achievable distortion exponents meet the upper bound for only certain ranges of the bandwidth ratio. We demonstrate that our results, which were derived for a complex Gaussian source, can be extended to more general source distributions as well.Comment: 36 pages, 11 figure