Real-time delay with network coding and feedback

Abstract

We consider the problem of minimizing delay when broadcasting over erasure channels with feedback. A sender wishes to communicate the same set of µ messages to several receivers. The sender can broadcast a single message or a combination (encoding) of messages to all receivers at each timestep, through separate erasure channels. Receivers provide feedback as to whether the transmission was received. If, at some time step, a receiver cannot identify a new message, delay is incurred. Our notion of delay is motivated by real-time applications that request progressively refined input, such as the successive refinement of an image encoded using multiple description coding.Our setup is novel because it combines coding techniques with feedback information to the end of minimizing delay. Uncoded scheduling or use of erasure correction coding, such as maximum distance separable (MDS) codes, has been well-studied in the literature. We show that our setup allows Θ(µ) benefits as compared to both previous approaches for offline algorithms, while feedback allows online algorithms to achieve smaller delay compared to online algorithms without feedback.Our main complexity results are that the offline minimization problem is N P -hard when the sender only schedules single messages and that the general problem remains N P -hard even when coding is allowed. However we show that coding does offer complexity gains by exhibiting specific classes of erasure instances that become trivial under coding schemes. We also discuss online heuristics and evaluate their performance through simulations.

Application-Layer Coding with Intermittent Feedback under Delay and Duty-Cycle Constraints

“…Coding over small blocks of information is investigated in [5] under the assumption of perfect feedback. In [6], a coding scheme over a large finite field (GF(256)) for delaysensitive multimedia applications is proposed.…”

Efficient network coding solutions for limiting the effect of packet loss

“…While NC increases throughput and lowers congestion, block decoding may cause major delays and reduction in the quality of service (QoS). Recent works have focused on QoS and proposed methods to reduce the average waiting time in the buffer of the intermediate nodes [28,29]. Our work differs from existing works in the sense that we use NC for data exchange activity and not for multicast purposes.…”

Adaptive Prioritized Random Linear Coding and Scheduling for Layered Data Delivery From Multiple Servers

“…Although the employment of RLC may result in large delay gains, scheduling of RLC encoded data is a NP-hard problem [19]. Since it is hard to find the optimal coding and scheduling solution, a number of practical solutions in wireless networks that exploit the feedback messages that are available to each network node are proposed in [12], [13], [22].…”

“…Unfortunately, digital Fountain codes such as Raptor codes and LT codes may perform poorly in terms of delay [19], [20]. To this aim, systematic Random Linear Codes (RLC) with feedback have been studied in [19] for minimizing the average delay in database replication systems. The feedback messages contain information about the packets that have been delivered to the receivers.…”