We consider a setting where a stream of qubits is processed sequentially. We derive fundamental limits on the rate at which classical information can be transmitted using qubits that decohere as they wait to be processed. Specifically, we model the sequential processing of qubits using a single server queue, and derive expressions for the classical capacity of such a quantum queue-channel.' Focusing on quantum erasures, we obtain an explicit single-letter capacity formula in terms of the stationary waiting time of qubits in the queue. Our capacity proof also implies that a classical' coding decoding strategy is optimal, i.e., an encoder which uses only orthogonal product states, and a decoder which measures in a fixed product basis, are sufficient to achieve the classical capacity of the quantum erasure queue-channel. More broadly, our work begins to quantitatively address the impact of decoherence on the performance limits of quantum information processing systems.
As an aside, we remark that the erasure queue-channel treated in @cite_8 can be used to model a multimedia-streaming scenario, where information packets become useless (erased) after a certain time.
@cite_8
2963352975 2127832277 1976407947 2963627748
An erasure broadcast network is considered with two disjoint sets of receivers: a set of weak receivers with all-equal erasure probabilities and equal cache sizes and a set of strong receivers with all-equal erasure probabilities and no cache memories. Lower and upper bounds are presented on the capacity-memory tradeoff of this network (the largest rate at which messages can be reliably communicated for given cache sizes). The lower bound is achieved by means of a joint cache-channel coding scheme and significantly improves over traditional schemes based on the separate cache-channel coding . In particular, it is shown that the joint cache-channel coding offers new global caching gains that scale with the number of strong receivers in the network. The upper bound uses bounding techniques from degraded broadcast channels and introduces an averaging argument to capture the fact that the contents of the cache memories are designed before knowing users’ demands. The derived upper bound is valid for all stochastically degraded broadcast channels. The lower and upper bounds match for a single weak receiver (and any number of strong receivers) when the cache size does not exceed a certain threshold. Improved bounds are presented for the special case of a single weak and a single strong receiver with two files and the bounds are shown to match over a large range of cache sizes. We analyze a simple network where a source and a receiver are connected by a line of erasure channels of different reliabilities. Recent prior work has shown that random linear network coding can achieve the min-cut capacity and therefore the asymptotic rate is determined by the worst link of the line network. In this paper we investigate the delay for transmitting a batch of packets, which is a function of all the erasure probabilities and the number of packets in the batch. We show a monotonicity result on the delay function and derive simple expressions which characterize the expected delay behavior of line networks. Further, we use a martingale bounded differences argument to show that the actual delay is tightly concentrated around its expectation. We consider a cognitive radio network where multiple secondary users (SUs) contend for spectrum usage, using random access, over available primary user (PU) channels. Our focus is on SUs' queueing delay performance, for which a systematic understanding is lacking. We take a fluid queue approximation approach to study the steady-state delay performance of SUs, for cases with a single PU channel and multiple PU channels. Using stochastic fluid models, we represent the queue dynamics as Poisson driven stochastic differential equations, and characterize the moments of the SUs' queue lengths accordingly. Since in practical systems, a secondary user would have no knowledge of other users' activities, its contention probability has to be set based on local information. With this observation, we develop adaptive algorithms to find the optimal contention probability that minimizes the mean queue lengths. Moreover, we study the impact of multiple channels and multiple interfaces, on SUs' delay performance. As expected, the use of multiple channels and or multiple interfaces leads to significant delay reduction. For a packet erasure broadcast channel with three receivers, we propose a new coding algorithm that makes use of feedback to dynamically adapt the code. Our algorithm is throughput optimal, and we conjecture that it also achieves an asymptotically optimal average decoding delay at the receivers. We consider heavy traffic asymptotics, where the load factor rho approaches 1 from below with either the arrival rate (lambda) or the channel parameter (mu) being fixed at a number less than 1. We verify through simulations that our algorithm achieves an asymptotically optimal decoding delay of O (1 1-rho).