High-SNR Analysis of Outage-Limited Communications With Bursty and Delay-Limited Information

Abstract

Abstract-This work analyzes the high-SNR asymptotic error performance of outage-limited communications with fading, where the number of bits that arrive at the transmitter during any time slot is random but the delivery of bits at the receiver must adhere to a strict delay limitation. Specifically, bit errors are caused by erroneous decoding at the receiver or violation of the strict delay constraint. Under certain scaling of the statistics of the bit-arrival process with SNR, this paper shows that the optimal decay behavior of the asymptotic total probability of bit error depends on how fast the burstiness of the source scales down with SNR. If the source burstiness scales down too slowly, the total probability of error is asymptotically dominated by delay-violation events. On the other hand, if the source burstiness scales down too quickly, the total probability of error is asymptotically dominated by channel-error events. However, at the proper scaling, where the burstiness scales linearly with 1 √ log SNR and at the optimal coding duration and transmission rate, the occurrences of channel errors and delay-violation errors are asymptotically balanced. In this latter case, the optimal exponent of the total probability of error reveals a tradeoff that addresses the question of how much of the allowable time and rate should be used for gaining reliability over the channel and how much for accommodating the burstiness with delay constraints.

Proactive multicasting with predictable demands

“…Thus, letting q(n) ∈ {1, · · · , Q(n)} denote the identifier of requests arriving in time slot n and T denotes the number of slots allowed to serve those requests so that request q(n) arriving in slot n has a deadline slot of D q(n) = n + T . Hence, scheduling the requests of the predictive network can be considered as a scheduling problem with deadlines, e.g., [3], [4].…”

Many-Sources Large Deviations for Max-Weight Scheduling

“…This asymptote usually gives a more refined approximation to the probabilistic quantities of interest by incorporating the impact of the multiplexing gain [16]- [39] obtained by averaging many traffic sources together. However, our interest in the "many-sources" asymptotic has also been fueled by our earlier work [40] on 2) a cross-layer optimization of the PHY layer parameters, e.g., duration of the finite code blocks or cooperative cluster size when the fading channel is operated at high signal-to-noise-ratio (SNR). The high SNR regime is a very natural setting for the many-sources scaling since the capacity of the channel typically scales to infinity as log(SNR), and therefore it is natural to scale the arrival rate of the flows with the same parameter, which is best accomplished by multiplexing more sources; in other words by setting L ∝ log(SNR).…”

“…Both of these are for an average of i.i.d. compound Poisson source processes with exponential packet size where the packet arrivals follow Poisson distribution of rate λ and the average packet size is 1/µ (see [40]). The function Λ * for this process is given by…”

Optimal code length for bursty sources with deadlines

“…In the context of communication over fading channels and CSI being available at the transmitter, [3] establishes a joint queuingcoding exponent with a streaming code while [5] studies the tradeoff between average delay and average power for reliable communication. While some papers consider the average delay performance e.g [6] or [8], our work resembles [3] and [5] in that it focuses on the asymptotic error exponent for a known delay budget D. Our work is closest to [4] which considers the SNR exponent in the absence of of CSI and request for retransmissions.…”