On the rate loss and construction of source codes for broadcast channels

In this paper, we first define and bound the rate loss of source codes for broadcast channels. Our broadcast channel model comprises one transmitter and two receivers; the transmitter is connected to each receiver by a private channel and to both receivers by a common channel. The transmitter sends a description of source (X, Y) through these channels, receiver 1 reconstructs X with distortion D1, and receiver 2 reconstructs Y with distortion D2. Suppose the rates of the common channel and private channels 1 and 2 are R0, R1, and R2, respectively. The work of Gray and Wyner gives a complete characterization of all achievable rate triples (R0,R1,R2) given any distortion pair (D1,D2). In this paper, we define the rate loss as the gap between the achievable region and the outer bound composed by the rate-distortion functions, i.e., R0+R1+R2 ≥ RX,Y (D1,D2), R0 + R1 ≥ RX(D1), and R0 + R2 ≥ RY (D2). We upper bound the rate loss for general sources by functions of distortions and upper bound the rate loss for Gaussian sources by constants, which implies that though the outer bound is generally not achievable, it may be quite close to the achievable region. This also bounds the gap between the achievable region and the inner bound proposed by Gray and Wyner and bounds the performance penalty associated with using separate decoders rather than joint decoders. We then construct such source codes using entropy-constrained dithered quantizers. The resulting implementation has low complexity and performance close to the theoretical optimum. In particular, the gap between its performance and the theoretical optimum can be bounded from above by constants for Gaussian sources

Myopic Coding in Multiple Relay Channels

In this paper, we investigate achievable rates for data transmission from sources to sinks through multiple relay networks. We consider myopic coding, a constrained communication strategy in which each node has only a local view of the network, meaning that nodes can only transmit to and decode from neighboring nodes. We compare this with omniscient coding, in which every node has a global view of the network and all nodes can cooperate. Using Gaussian channels as examples, we find that when the nodes transmit at low power, the rates achievable with two-hop myopic coding are as large as that under omniscient coding in a five-node multiple relay channel and close to that under omniscient coding in a six-node multiple relay channel. These results suggest that we may do local coding and cooperation without compromising much on the transmission rate. Practically, myopic coding schemes are more robust to topology changes because encoding and decoding at a node are not affected when there are changes at remote nodes. Furthermore, myopic coding mitigates the high computational complexity and large buffer/memory requirements of omniscient coding.Comment: To appear in the proceedings of the 2005 IEEE International Symposium on Information Theory, Adelaide, Australia, September 4-9, 200

Bounding the energy-constrained quantum and private capacities of phase-insensitive bosonic Gaussian channels

We establish several upper bounds on the energy-constrained quantum and private capacities of all single-mode phase-insensitive bosonic Gaussian channels. The first upper bound, which we call the \u27data-processing bound,\u27 is the simplest and is obtained by decomposing a phase-insensitive channel as a pure-loss channel followed by a quantum-limited amplifier channel. We prove that the data-processing bound can be at most 1.45 bits larger than a known lower bound on these capacities of the phase-insensitive Gaussian channel. We discuss another data-processing upper bound as well. Two other upper bounds, which we call the \u27ϵ-degradable bound\u27 and the \u27ϵ-close-degradable bound,\u27 are established using the notion of approximate degradability along with energy constraints. We find a strong limitation on any potential superadditivity of the coherent information of any phase-insensitive Gaussian channel in the low-noise regime, as the data-processing bound is very near to a known lower bound in such cases. We also find improved achievable rates of private communication through bosonic thermal channels, by employing coding schemes that make use of displaced thermal states. We end by proving that an optimal Gaussian input state for the energy-constrained, generalized channel divergence of two particular Gaussian channels is the two-mode squeezed vacuum state that saturates the energy constraint. What remains open for several interesting channel divergences, such as the diamond norm or the Rényi channel divergence, is to determine whether, among all input states, a Gaussian state is optimal

Distributed MIMO Systems with Oblivious Antennas

A scenario in which a single source communicates with a single destination via a distributed MIMO transceiver is considered. The source operates each of the transmit antennas via finite-capacity links, and likewise the destination is connected to the receiving antennas through capacity-constrained channels. Targeting a nomadic communication scenario, in which the distributed MIMO transceiver is designed to serve different standards or services, transmitters and receivers are assumed to be oblivious to the encoding functions shared by source and destination. Adopting a Gaussian symmetric interference network as the channel model (as for regularly placed transmitters and receivers), achievable rates are investigated and compared with an upper bound. It is concluded that in certain asymptotic and non-asymptotic regimes obliviousness of transmitters and receivers does not cause any loss of optimality.Comment: In Proc. of the 2008 IEEE International Symposium on Information Theory (ISIT 2008), Toronto, Ontario, Canad

Code designs for MIMO broadcast channels

Recent information-theoretic results show the optimality of dirty-paper coding (DPC) in achieving the full capacity region of the Gaussian multiple-input multiple-output (MIMO) broadcast channel (BC). This paper presents a DPC based code design for BCs. We consider the case in which there is an individual rate/signal-to-interference-plus-noise ratio (SINR) constraint for each user. For a fixed transmitter power, we choose the linear transmit precoding matrix such that the SINRs at users are uniformly maximized, thus ensuring the best bit-error rate performance. We start with Cover's simplest two-user Gaussian BC and present a coding scheme that operates 1.44 dB from the boundary of the capacity region at the rate of one bit per real sample (b/s) for each user. We then extend the coding strategy to a two-user MIMO Gaussian BC with two transmit antennas at the base-station and develop the first limit-approaching code design using nested turbo codes for DPC. At the rate of 1 b/s for each user, our design operates 1.48 dB from the capacity region boundary. We also consider the performance of our scheme over a slow fading BC. For two transmit antennas, simulation results indicate a performance loss of only 1.4 dB, 1.64 dB and 1.99 dB from the theoretical limit in terms of the total transmission power for the two, three and four user case, respectively

Maximum tolerable excess noise in CV-QKD and improved lower bound on two-way capacities

The two-way capacities of quantum channels determine the ultimate entanglement distribution rates achievable by two distant parties that are connected by a noisy transmission line, in absence of quantum repeaters. Since repeaters will likely be expensive to build and maintain, a central open problem of quantum communication is to understand what performances are achievable without them. In this paper, we find a new lower bound on the energy-constrained and unconstrained two-way quantum and secret-key capacities of all phase-insensitive bosonic Gaussian channels, namely thermal attenuator, thermal amplifier, and additive Gaussian noise, which are realistic models for the noise affecting optical fibres or free-space links. Ours is the first nonzero lower bound in the parameter range where the (reverse) coherent information becomes negative, and it shows explicitly that entanglement distribution is always possible when the channel is not entanglement breaking. In addition, our construction is fully explicit, i.e. we devise and optimise a concrete entanglement distribution and distillation protocol that works by combining recurrence and hashing protocols.Comment: 41 pages, 11 figure