Completion of codes with finite bi-decoding delays

AbstractLet A∗ be a free monoid generated by a set A and let X⊆A∗ be a code with property P. The embedding of X into a complete code Y⊆A∗ with the same property P is called the completion of X. The method of completion of rational bifix codes and codes with finite decoding delays have been investigated by a number of authors. In this paper, we provide a general method of construction for completing the codes with finite bi-decoding delays. As a consequence, the completion method of rational bifix codes and codes with finite decoding delays is extended and applied to codes with finite bi-decoding delays

Reliable Transmission of Short Packets through Queues and Noisy Channels under Latency and Peak-Age Violation Guarantees

This work investigates the probability that the delay and the peak-age of information exceed a desired threshold in a point-to-point communication system with short information packets. The packets are generated according to a stationary memoryless Bernoulli process, placed in a single-server queue and then transmitted over a wireless channel. A variable-length stop-feedback coding scheme---a general strategy that encompasses simple automatic repetition request (ARQ) and more sophisticated hybrid ARQ techniques as special cases---is used by the transmitter to convey the information packets to the receiver. By leveraging finite-blocklength results, the delay violation and the peak-age violation probabilities are characterized without resorting to approximations based on large-deviation theory as in previous literature. Numerical results illuminate the dependence of delay and peak-age violation probability on system parameters such as the frame size and the undetected error probability, and on the chosen packet-management policy. The guidelines provided by our analysis are particularly useful for the design of low-latency ultra-reliable communication systems.Comment: To appear in IEEE journal on selected areas of communication (IEEE JSAC

On the Performance of Short Block Codes over Finite-State Channels in the Rare-Transition Regime

As the mobile application landscape expands, wireless networks are tasked with supporting different connection profiles, including real-time traffic and delay-sensitive communications. Among many ensuing engineering challenges is the need to better understand the fundamental limits of forward error correction in non-asymptotic regimes. This article characterizes the performance of random block codes over finite-state channels and evaluates their queueing performance under maximum-likelihood decoding. In particular, classical results from information theory are revisited in the context of channels with rare transitions, and bounds on the probabilities of decoding failure are derived for random codes. This creates an analysis framework where channel dependencies within and across codewords are preserved. Such results are subsequently integrated into a queueing problem formulation. For instance, it is shown that, for random coding on the Gilbert-Elliott channel, the performance analysis based on upper bounds on error probability provides very good estimates of system performance and optimum code parameters. Overall, this study offers new insights about the impact of channel correlation on the performance of delay-aware, point-to-point communication links. It also provides novel guidelines on how to select code rates and block lengths for real-time traffic over wireless communication infrastructures

Delay Minimization for Instantly Decodable Network Coding in Persistent Channels with Feedback Intermittence

In this paper, we consider the problem of minimizing the multicast decoding delay of generalized instantly decodable network coding (G-IDNC) over persistent forward and feedback erasure channels with feedback intermittence. In such an environment, the sender does not always receive acknowledgement from the receivers after each transmission. Moreover, both the forward and feedback channels are subject to persistent erasures, which can be modelled by a two state (good and bad states) Markov chain known as Gilbert-Elliott channel (GEC). Due to such feedback imperfections, the sender is unable to determine subsequent instantly decodable packets combination for all receivers. Given this harsh channel and feedback model, we first derive expressions for the probability distributions of decoding delay increments and then employ these expressions in formulating the minimum decoding problem in such environment as a maximum weight clique problem in the G-IDNC graph. We also show that the problem formulations in simpler channel and feedback models are special cases of our generalized formulation. Since this problem is NP-hard, we design a greedy algorithm to solve it and compare it to blind approaches proposed in literature. Through extensive simulations, our adaptive algorithm is shown to outperform the blind approaches in all situations and to achieve significant improvement in the decoding delay, especially when the channel is highly persisten

Download and Access Trade-offs in Lagrange Coded Computing

Lagrange Coded Computing (LCC) is a recently proposed technique for resilient, secure, and private computation of arbitrary polynomials in distributed environments. By mapping such computations to composition of polynomials, LCC allows the master node to complete the computation by accessing a minimal number of workers and downloading all of their content, thus providing resiliency to the remaining stragglers. However, in the most common case in which the number of stragglers is less than in the worst case scenario, much of the computational power of the system remains unexploited. To amend this issue, in this paper we expand LCC by studying a fundamental trade-off between download and access, and present two contributions. In the first contribution, it is shown that without any modification to the encoding process, the master can decode the computations by accessing a larger number of nodes, however downloading less information from each node in comparison with LCC (i.e., trading access for download). This scheme relies on decoding a particular polynomial in the ideal that is generated by the polynomials of interest, a technique we call Ideal Decoding. This new scheme also improves LCC in the sense that for systems with adversaries, the overall downloaded bandwidth is smaller than in LCC. In the second contribution we study a real-time model of this trade-off, in which the data from the workers is downloaded sequentially. By clustering nodes of similar delays and encoding the function with Universally Decodable Matrices, the master can decode once sufficient data is downloaded from every cluster, regardless of the internal delays within that cluster. This allows the master to utilize the partial work that is done by stragglers, rather than to ignore it, a feature that most past works in coded computing are lacking