We consider a queue-channel model that captures the waiting time-dependent degradation of information bits as they wait to be transmitted. Such a scenario arises naturally in quantum communications, where information bits become useless after a certain time. Trailing the capacity results obtained recently for certain queue-channels, this paper aims to construct practical channel codes for the erasure queue-channel (EQC)—a channel characterized by highly correlated erasures, governed by the underlying queuing dynamics. Our main contributions in this paper are twofold: (i) We propose a generic ‘wrapper’ based on interleaving across renewal blocks of the queue to convert any capacity-achieving code for a memoryless erasure channel to a capacity-achieving code for the EQC. Next, due to the complexity involved in implementing interleaved systems, (ii) we study the performance of LDPC and Polar codes without any interleaving. Motivated by the empirical performance, we show that standard Arıkan’s Polar transform polarizes the M/M/1 EQC.
We consider a queue-channel model that captures the waiting time-dependent degradation of information bits as they wait to be transmitted. Such a scenario arises naturally in quantum communications, where information bits become useless after a certain time. Trailing the capacity results obtained recently for certain queue-channels, this paper aims to construct practical channel codes for the erasure queue-channel (EQC)—a channel characterized by highly correlated erasures, governed by the underlying queuing dynamics. Our main contributions in this paper are twofold: (i) We propose a generic ‘wrapper’ based on interleaving across renewal blocks of the queue to convert any capacity-achieving code for a memoryless erasure channel to a capacity-achieving code for the EQC. Next, due to the complexity involved in implementing interleaved systems, (ii) we study the performance of LDPC and Polar codes without any interleaving. Motivated by the empirical performance, we show that standard Arıkan’s Polar transform polarizes the M/M/1 EQC.
We consider a queue-channel model that captures the waiting time-dependent degradation of information bits as they wait to be transmitted. Such a scenario arises naturally in quantum communications, where quantum bits tend to decohere rapidly. Trailing the capacity results obtained recently for certain queue-channels, this paper aims to construct practical channel codes for the erasure queue-channel (EQC)—a channel characterized by highly correlated erasures, governed by the underlying queuing dynamics. Our main contributions in this paper are twofold: (i) We propose a generic ‘wrapper’ based on interleaving across renewal blocks of the queue to convert any capacity-achieving block code for a memoryless erasure channel to a capacity-achieving code for the EQC. Next, due to the complexity involved in implementing interleaved systems, (ii) we study the performance of LDPC and Polar codes without any interleaving. We show that standard Arıkan’s Polar transform polarizes the EQC for certain restricted class of erasure probability functions. We also highlight some possible approaches and the corresponding challenges involved in proving the polarization of a general EQC.
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.
A queue-channel is a model that captures waiting time-dependent degradation of information bits—a scenario motivated by quantum communications and delay-sensitive streaming. Recent work has characterised the capacity of the erasure queue-channel [1], and other noise models encountered in quantum communications. In this paper, we study an erasure queue-channel with feedback, and ask after the optimal transmission strategy to minimize waiting-induced erasures. Specifically, we assume that instantaneous feedback of queue-length (or of the queue-channel output) is available at the transmitter, which can modulate the rate of Poisson transmissions into the queue-channel. We pose an optimal control problem using HJB-style equations to maximize the information capacity, when the transmitter can choose from a bounded set of transmission rates. We show (under a numerically verifiable condition) that the optimal transmission policy is a single-threshold policy of the bang-bang type. In other words, transmitting at the maximum (minimum) possible rate when the queue is below (above) a threshold, maximizes the information capacity of the erasure queue-channel with feedback.
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 two important noise models, namely the erasure channel and the depolarizing channel, we obtain explicit single-letter capacity formulas 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 both queue-channels. Our proof technique for the converse theorem generalizes readily - in particular, whenever the underlying quantum noise channel is additive, we can obtain a single-letter upper bound on the classical capacity of the corresponding quantum queue-channel. More broadly, our work begins to quantitatively address the impact of decoherence on the performance limits of quantum information processing systems.
We consider classical-quantum (cq-)channels with memory, and establish that Arıkan-constructed polar codes achieve the classical capacity for two key noise models, namely for (i) qubit erasures and (ii) unital qubit noise with channel state information at the receiver. The memory in the channel is assumed to be governed by a discrete-time, countable-state, aperiodic, irreducible, and positive recurrent Markov process. We establish this result by leveraging classical polar coding guarantees established for finite-state, aperiodic, and irreducible Markov processes [FAIM] in [1], alongside the finding that no entanglement is required to achieve the capacity of Markovian unital and erasure quantum channels when transmitting classical information [2], [3]. More broadly, our work illustrates that for cq-channels with memory, where an optimal coding strategy is essentially classical, polar codes can be shown to approach the capacity.
Quantum queue-channels arise naturally in the context of buffering in quantum networks, wherein the noise suffered by the quantum states depends on the time spent waiting in the buffer. Mandayam (2020) derived a simple upper bound on the classical capacity of an additive queue-channel and showed it to be achievable for the erasure and depolarizing channels. In this article, we characterize the classical capacity for the class of unital qubit queue-channels and show that a simple product (nonentangled) decoding strategy is capacity achieving. As an intermediate step, we present a simpler derivation of an explicit capacity-achieving product decoding strategy for any independent identically distributed unital qubit channel, which may be of interest. As an important special case, we also derive the capacity and optimal decoding strategies for a symmetric generalized amplitude damping queue-channel. Our results provide useful insights toward designing practical quantum communication networks and highlight the need to explicitly model the impact of buffering.