Normalized Delivery Time Research Articles

Normalized Delivery Time of Wireless MapReduce

Normalized Delivery Time of Wireless MapReduce

Fundamental Limits of Cache-Aided MIMO Wireless Networks

This paper studies the Multi-Input-Multi-Output (MIMO) interference networks with arbitrary number of transmitters and receivers, where both the transmitters and receivers are equipped with caches. The main goal is to design content placement and delivery schemes that minimize the worst case normalized delivery time (NDT). First, we propose a delivery scheme for the cache-aided Single-Input-Multiple-Output (SIMO) interference networks. Then, we obtain the achievable NDT of the cache-aided MIMO interference networks using the decomposition property of splitting each multi-antenna transmitter into multiple single antenna transmitters. Furthermore, we derive an information-theoretic bound on the optimal NDT of the cache-aided MIMO interference network. Analytical results show that the proposed scheme is within a multiplicative gap of 2 from the derived lower bound independent of all system parameters for any uncoded cache placement scheme. We also derive a novel delivery scheme for the cache-aided Multi-Input-Single-Output (MISO) interference network outperforming our proposed scheme for the cache-aided MIMO interference network. The numerical results show the superiority of our proposed scheme over the state-of-the-art schemes in the literature. Our results show that the coded caching gain has a more significant contribution in reducing the transmission latency than the spatial multiplexing gain. Our results indicate that the receive-antennas become more effective in reducing the NDT than the transmit-antennas in the presence of caches at the receiver-side. In addition, we show that increasing the number of transmit-antennas has a higher gain in reducing the NDT than adding more transmitters in the cache-aided MISO interference network.

An Analytical Framework for Delay Optimal Mobile Edge Deployment in Wireless Networks

The emerging edge caching provides an effective way to reduce service delay for mobile users. However, due to high deployment cost of edge hosts, a practical problem is how to achieve minimum delay under a proper edge deployment strategy. In this letter, we provide an analytical framework for delay optimal mobile edge deployment in a partially connected wireless network, where the request files can be cached at the edge hosts and cooperatively transmitted through multiple base stations. In order to deal with the heterogeneous transmission requirements, we separate the entire transmission into backhaul and wireless phases, and propose average user normalized delivery time (AUNDT) as the performance metric. On top of that, we characterize the trade-off relations between the proposed AUNDT and other network deployment parameters. Using the proposed analytical framework, we are able to provide the optimal mobile edge deployment strategy in terms of AUNDT, which provides a useful guideline for future mobile edge deployment.

Online Caching With Wireless Fronthauling and Delivery in Fog-Aided Networks

Fog Radio Access Network (F-RAN) exploits cached contents at edge nodes (ENs) and fronthaul connection to the cloud for content delivery. Assuming dedicated fronthaul links between cloud and each EN, previous works focused on analyses of F-RANs using offline or online caching depending whether the content popularity is time-invariant or time-variant. Extension has been done for multicast fronthaul link connecting cloud to only two ENs and time-invariant popularity. In contrast, the scope of this work is on the case where multicast fronthaul link connects arbitrary number of ENs to the cloud and content popularity is time-variant. Normalized Delivery Time (NDT) is used as a performance measure and by investigating proactive online caching, analytical results reveal that the power scaling of fronthaul transmission sets a limit on the performance of F-RAN.

Prevalence of Cytomegalovirus in First Trimesteric Spontaneous Abortion: A Prospective Serological and Molecular Case–control Study

Aim: To measure the prevalence and assess the risk of cytomegalovirus (CMV) infection in women diagnosed with first-trimester spontaneous abortion. Comparison Methods: This was a prospective case-control study; a total of 551 women were recruited from two Maternity and Children Hospitals (Makkah and Jeddah cities) in the Western province of the kingdom between March 2013 and June 2016 Serum and products of conceptions were collected prospectively from 201 women diagnosed with first-trimester spontaneous abortion. Another set of serum samples and placental tissues were collected from 350 healthy pregnant women at the time of normal vaginal delivery. CMV IgM and IgG antibodies were measured serologically by ELISA while viral DNA was detected in tissue specimens by PCR. Socio-economic data were analysed to identify potential risk factors of abortion and/or CMV infection. Results: The overall prevalence was 88.4%, 13.6% and 10.1%, for IgG+, IgM+ and PCR+, respectively. IgG+ frequency was comparable between cases (89%) and controls (88%). Both exclusively IgM+ (7.9% vs. 0.6%) and dual IgM+/IgG+ (22.4% vs. 3.4%) antibodies were significantly more prevalent in abortion (P < 0.01). PCR+ was also significantly higher (P < 0.01) in abortion (25.4% vs. 1.4%). Women with exclusive IgM+ (OR 17.1; 95%CI [3.38 – 86.68]; P = 0.001) and those who were positive for all tests (OR 29.3; 95%CI [6.52–131.71]; P < 0.001) had a significantly increased risk for abortion. Conclusions: The majority of the study sample of pregnant women in Saudi Arabia were previously exposed to CMV. First trimester CMV infection appears to be an independent risk for spontaneous abortion and viral spread to the intrauterine cavity was associated with the highest risk for miscarriage. More studies are required to measure the precise prevalence of CMV and its associated sequelae during pregnancy in the kingdom.

How Much Can D2D Communication Reduce Content Delivery Latency in Fog Networks With Edge Caching?

A Fog-Radio Access Network (F-RAN) is studied in which cache-enabled Edge Nodes (ENs) with dedicated fronthaul connections to the cloud aim at delivering contents to mobile users. Using an information-theoretic approach, this work tackles the problem of quantifying the potential latency reduction that can be obtained by enabling Device-to-Device (D2D) communication over out-of-band broadcast links. Following prior work, the Normalized Delivery Time (NDT) — a metric that captures the high signal-to-noise ratio worst-case latency — is adopted as the performance criterion of interest. Joint edge caching, downlink transmission, and D2D communication policies based on compress-and-forward are proposed that are shown to be information-theoretically optimal to within a constant multiplicative factor of two for all values of the problem parameters, and to achieve the minimum NDT for a number of special cases. The analysis provides insights on the role of D2D cooperation in improving the delivery latency.

Content Caching and Delivery in MIMO Fog-RANs With Wireless Fronthaul at Small Cache Size

This letter investigates the caching and delivery strategies in a multiple-input multiple-output (MIMO) fog radio access network (Fog-RAN). We focus on the small cache size scenario where the accumulated cache memories of all edge nodes (ENs) are not enough to cache the whole database. We propose a new file splitting and placement scheme tailored for the small cache size, which offers the freedom to adjust the duplication order of the cached contents to minimize the normalized delivery time (NDT). In the fronthaul delivery, we use multiple antennas to multiplex multiple messages while in the access delivery, transmitter cooperation induced by the duplicated contents among ENs is utilized to cancel interference. By jointly optimizing caching and delivery, we obtain an achievable minimum NDT. It is shown that the achievable NDT is within an additive gap of 1 to the theoretical optimum.

Cache-Aided Interference Management in Partially Connected Linear Networks

This paper studies caching in (K+L-1) x K partially connected wireless linear networks, where each of the K receivers locally communicates with L out of the K+L-1 transmitters, and caches are at all nodes. The goal is to design caching and delivery schemes to reduce the transmission latency, by using normalized delivery time (NDT) as the performance metric. For small transmitter cache size (any L transmitters can collectively store the database just once), we propose a cyclic caching strategy so that each of every L consecutive transmitters caches a distinct part of each file; the delivery strategy exploits coded multicasting and interference alignment by introducing virtual receivers. The obtained NDT is within a multiplicative gap of 2 to the optimum in the entire cache size region, and optimal in certain region. For large transmitter cache size (any L transmitters can collectively store the database for multiple copies), we propose a modified caching strategy so that every bit is repeatedly cached at consecutive transmitters; the delivery strategy exploits self-interference cancellation and interference neutralization. By combining these schemes, the NDT is optimal in a larger region. We also extend our results to linear networks with heterogeneous receiver connectivity and partially connected circular networks.

Cache-Aided Combination Networks With Interference

Centralized coded caching and delivery is studied for a radio access combination network (RACN), whereby a set of H edge nodes (ENs), connected to a cloud server via orthogonal fronthaul links with limited capacity, serve a total of K user equipments (UEs) over wireless links. The cloud server is assumed to hold a library of N files, each of size F bits; and each user, equipped with a cache of size $\mu _{\text {R}} {\it\text { N F}}$ bits, is connected to a distinct set of r ENs each of which equipped with a cache of size $\mu _{\text {T}} {\it\text { N F}}$ bits, where $\mu _{\text {T}}$ , $\mu _{\text {R}} \in [{0,1}]$ are the fractional cache capacities of the UEs and the ENs, respectively. The objective is to minimize the normalized delivery time (NDT), which refers to the worst case delivery latency when each user requests a single distinct file from the library. Three coded caching and transmission schemes are considered, namely the MDS-IA , soft-transfer and zero-forcing (ZF) schemes. MDS-IA utilizes maximum distance separable (MDS) codes in the placement phase and real interference alignment (IA) in the delivery phase. The achievable NDT for this scheme is presented for $\text {r}=2$ and arbitrary fractional cache sizes $\mu _{\text {T}}$ and $\mu _{\text {R}}$ , and also for arbitrary value of r and fractional cache size $\mu _{\text {T}}$ when the cache capacity of the UE is above a certain threshold. The soft-transfer scheme utilizes soft-transfer of coded symbols to ENs that implement ZF over the edge links. The achievable NDT for this scheme is presented for arbitrary r and arbitrary fractional cache sizes $\mu _{\text {T}}$ and $\mu _{\text {R}}$ . The last scheme utilizes ZF between the ENs and the UEs without the participation of the cloud server in the delivery phase. The achievable NDT for this scheme is presented for an arbitrary value of r when the total cache size at a pair of UE and EN is sufficient to store the whole library, i.e., $\mu _{\text {T}}+\mu _{\text {R}} \geq 1$ . The results indicate that the fronthaul capacity determines which scheme achieves a better performance in terms of the NDT, and the soft-transfer scheme becomes favorable as the fronthaul capacity increases.

Fundamental Limits of Memory-Latency Tradeoff in Fog Radio Access Networks Under Arbitrary Demands

We consider a fog radio access network (F-RAN) with multiple transmitters and receivers, where each transmitter is connected to the cloud via a fronthaul link. Each network node has a finite cache, where it fills its cache with portions of the library files in the off-peak hours. In the delivery phase, receivers request each library files according to an arbitrary popularity distribution. The cloud and the transmitters are responsible for satisfying the requests. This paper aims to design content placement and coded delivery schemes for minimizing both the expected normalized delivery time (NDT) and the peak NDT which measures the transmission latency. We propose achievable transmission policies, and derive an information-theoretic bound on the expected NDT under uniform popularity distribution. The analytical results show that the proposed scheme is within a gap of 2.58 from the derived bound for both the expected NDT under uniform popularity distribution and the peak NDT. Next, we investigate the expected NDT under an arbitrary popularity distribution for an F-RAN with transmitter-side caches only. The achievable and information-theoretic bounds on the expected NDT are derived, where we analytically prove that our proposed scheme is optimal within a gap of two independent of the popularity distribution.

Treating Content Delivery in Multi-Antenna Coded Caching as General Message Sets Transmission: A DoF Region Perspective

Coded caching can create coded multicasting thus significantly accelerates content delivery in broadcast channels with receiver caches. While the original delivery scheme in coded caching multicasts each coded message sequentially, it is not optimal for multiple-input multiple-output (MIMO) broadcast channels. This work aims to investigate the full spatial multiplexing gain in multi-antenna coded caching by transmitting all coded messages concurrently. In specific, we propose to treat the content delivery as the transmission problem with general message sets where all possible messages are present, each with different length and intended for different user set. We first obtain inner and outer bounds of the degrees of freedom (DoF) region of a $K$-user $(M,N)$ broadcast channel with general message sets, with $M$ and $N$ being the number of transmit and receive antennas, respectively. Then for any given set of coded messages, we find its minimum normalized delivery time (NDT) by searching the optimal DoF tuple in the DoF regions. The obtained minimum NDT is optimal at antenna configuration $\frac{M}{N} \in (0,1]\cup[K, \infty)$ and is within a multiplicative gap of $\frac{M}{N}$ to optimum at $\frac{M}{N} \in (1,K)$. Our NDT results can be evaluated for any user demand with both centralized and decentralized cache placement.

Fundamental Limits of Cloud and Cache-Aided Interference Management With Multi-Antenna Edge Nodes

In fog-aided cellular systems, content delivery latency can be minimized by jointly optimizing edge caching and transmission strategies. In order to account for the cache capacity limitations at the Edge Nodes (ENs), transmission generally involves both fronthaul transfer from a cloud processor with access to the content library to the ENs, as well as wireless delivery from the ENs to the users. In this paper, the resulting problem is studied from an information-theoretic viewpoint by making the following practically relevant assumptions: 1) the ENs have multiple antennas; 2) only uncoded fractional caching is allowed; 3) the fronthaul links are used to send fractions of contents; and 4) the ENs are constrained to use one-shot linear precoding on the wireless channel. Assuming offline proactive caching and focusing on a high signal-to-noise ratio (SNR) latency metric, the optimal information-theoretic performance is investigated under both serial and pipelined fronthaul-edge transmission modes. The analysis characterizes the minimum high-SNR latency in terms of Normalized Delivery Time (NDT) for worst-case users' demands. The characterization is exact for a subset of system parameters, and is generally optimal within a multiplicative factor of 3/2 for the serial case and of 2 for the pipelined case. The results bring insights into the optimal interplay between edge and cloud processing in fog-aided wireless networks as a function of system resources, including the number of antennas at the ENs, the ENs' cache capacity and the fronthaul capacity.

Cache-Assisted Broadcast-Relay Wireless Networks: A Delivery-Time Cache-Memory Tradeoff

An emerging trend of next generation communication systems is to deploy caches at network edges to reduce file delivery latency. To investigate this aspect, we study the fundamental limits of a cache-aided broadcast-relay wireless network consisting of one central base station, $M$ cache-equipped transceivers and $K$ receivers from a latency-centric perspective. We use the normalized delivery time (NDT) to capture the per-bit latency at high signal-to-noise ratio (SNR). The objective is to jointly design the cache placement and file delivery in order to minimize the NDT. To this end, we establish two converse results and two achievability schemes. The first converse result is restricted to one-shot delivery schemes, while the second excludes this restriction. Similarly, the first achievable scheme is a general NDT-optimal one-shot scheme that synergistically exploits both multicasting and distributed zero-forcing opportunities. With respect to the second converse result, this scheme performs well for various parameter settings, particularly at higher cache sizes. The second scheme, effective at lower cache sizes, designs beamformers to facilitate both subspace interference alignment and zero-forcing. Exploiting both schemes, we are able to characterize the optimal tradeoff between cache storage and latency in networks satisfying $K+M\leq 4$ . The tradeoff illustrates that the NDT is the preferred choice to capture the latency of a system rather than the commonly used sum degrees of freedom (DoF). In fact, our optimal tradeoff refutes the popular belief that increasing cache sizes translates to increasing the achievable sum DoF. As such, we discuss cases where increasing cache sizes decreases both the delivery time and the achievable DoF.

Online Edge Caching and Wireless Delivery in Fog-Aided Networks With Dynamic Content Popularity

Fog radio access network (F-RAN) architectures can leverage both cloud processing and edge caching for content delivery to the users. To this end, F-RAN utilizes caches at the edge nodes (ENs) and fronthaul links connecting a cloud processor to ENs. Assuming time-invariant content popularity, existing information-theoretic analyses of content delivery in F-RANs rely on offline caching with separate content placement and delivery phases. In contrast, this paper focuses on the scenario in which the set of popular content is time-varying, hence necessitating the online replenishment of the ENs’ caches along with the delivery of the requested files. The analysis is centered on the characterization of the long-term normalized delivery time (NDT), which captures the temporal dependence of the coding latencies accrued across multiple time slots in the high signal-to-noise ratio regime. Online edge caching and delivery schemes are investigated for both serial and pipelined transmission modes across fronthaul and edge segments. Analytical results demonstrate that, in the presence of a time-varying content popularity, the rate of fronthaul links sets a fundamental limit on the long-term NDT of F-RAN system. Analytical results are further verified by numerical simulation, yielding important design insights.

Fundamental Tradeoff Between Storage and Latency in Cache-Aided Wireless Interference Networks

This paper studies the fundamental tradeoff between storage and latency in a general wireless interference network with caches equipped at all transmitters and receivers. The tradeoff is characterized by an information-theoretic metric, \emph{normalized delivery time} (NDT), which is the worst-case delivery time of the actual traffic load at a transmission rate specified by degrees of freedom (DoF) of a given channel. We obtain both an achievable upper bound and a theoretical lower bound of the minimum NDT for any number of transmitters, any number of receivers, and any feasible cache size tuple. We show that the achievable NDT is exactly optimal in certain cache size regions, and is within a bounded multiplicative gap to the theoretical lower bound in other regions. In the achievability analysis, we first propose a novel cooperative transmitter/receiver coded caching strategy. It offers the freedom to adjust file splitting ratios for NDT minimization. We then propose a delivery strategy which transforms the considered interference network into a new class of cooperative X-multicast channels. It leverages local caching gain, coded multicasting gain, and transmitter cooperation gain (via interference alignment and interference neutralization) opportunistically. Finally, the achievable NDT is obtained by solving a linear programming problem. This study reveals that with caching at both transmitter and receiver sides, the network can benefit simultaneously from traffic load reduction and transmission rate enhancement, thereby effectively reducing the content delivery latency.

Fog-Aided Wireless Networks for Content Delivery: Fundamental Latency Tradeoffs

A fog-aided wireless network architecture is studied in which edge-nodes (ENs), such as base stations, are connected to a cloud processor via dedicated fronthaul links, while also being endowed with caches. Cloud processing enables the centralized implementation of cooperative transmission strategies at the ENs, albeit at the cost of an increased latency due to fronthaul transfer. In contrast, the proactive caching of popular content at the ENs allows for the low-latency delivery of the cached files, but with generally limited opportunities for cooperative transmission among the ENs. The interplay between cloud processing and edge caching is addressed from an information-theoretic viewpoint by investigating the fundamental limits of a high Signal-to-Noise-Ratio (SNR) metric, termed normalized delivery time (NDT), which captures the worst-case coding latency for delivering any requested content to the users. The NDT is defined under the assumptions of either serial or pipelined fronthaul-edge transmission, and is studied as a function of fronthaul and cache capacity constraints. Placement and delivery strategies across both fronthaul and wireless, or edge, segments are proposed with the aim of minimizing the NDT. Information-theoretic lower bounds on the NDT are also derived. Achievability arguments and lower bounds are leveraged to characterize the minimal NDT in a number of important special cases, including systems with no caching capabilities, as well as to prove that the proposed schemes achieve optimality within a constant multiplicative factor of 2 for all values of the problem parameters.

Fundamental Storage-Latency Tradeoff in Cache-Aided MIMO Interference Networks

Caching is an effective technique to improve user perceived experience for content delivery in wireless networks. Wireless caching differs from traditional web caching in that it can exploit the broadcast nature of wireless medium and hence opportunistically change the network topologies. This paper studies a cache-aided MIMO interference network with 3 transmitters each equipped with M antennas and 3 receivers each with N antennas. With caching at both the transmitter and receiver sides, the network is changed to hybrid forms of MIMO broadcast channel, MIMO X channel, and MIMO multicast channels. We analyze the degrees of freedom (DoF) of these new channel models using practical interference management schemes. Based on the collective use of these DoF results, we then obtain an achievable normalized delivery time (NDT) of the network, an information-theoretic metric that evaluates the worst-case delivery time at given cache sizes. The obtained NDT is for arbitrary M, N and any feasible cache sizes. It is shown to be optimal in certain cases and within a multiplicative gap of 3 from the optimum in other cases. The extension to the network with arbitrary number of transmitters and receivers is also discussed.

Post B-lynch uterine rupture: case report and review of literature.

Postpartum hemorrhage (PPH) remains one of the three leading causes of maternal death and uterine atony accounts for 75–90 % of primary PPH. Apart from traditional conservative methods such as medical therapy, tamponades, the B-Lynch surgical technique has been widely used around the world. In 1997, Christopher B. Lynch devised these mechanical uterine compressing sutures to avoid hysterectomy in cases of severe PPH due to uterine atony, and since then, anecdotal evidence suggests that around 1,300 cases have been performed successfully worldwide including in India, Africa, North and South America, and Europe (Figs. 1, ​,22). Fig. 1 Ruptured uterus Fig. 2 Sutured uterus Case Report A 23-year G4P1L1A2 was admitted from casualty on November 5, 2011 with 4 months of amenorrhea and pain in the abdomen since the morning. She was very pale, had tachycardia, and a BP of 90/60 mmHg. There was abdominal tenderness and guarding. There was also a suprapubic transverse scar of a previous surgery. The uterine size could not be assessed due to extreme tenderness and guarding. At the time of the previous normal delivery, the patient had atonic PPH for which B-Lynch suturing was done. The suture material used for B-Lynch was Polyglactin No 1 (delayed absorbable suture material) on round body needle. The ultrasound showed moderate free fluid in the abdomen, the fetus lying outside the uterine cavity, and a 7 × 7 cm retro placental hemorrhage -s/o uterine rupture. Under general anesthesia, an exploratory laparotomy was performed. The uterine rupture was approximately 6 cm in length at the fundal region. The fetus with the amniotic sac lying out of ruptured site and around 1,500 ml of hemoperitoneum. The uterus was sutured with delayed absorbable sutures in three layers. Peritoneal lavage was given and an intraperitoneal drain was kept. The uterine height was marked and monitored postoperatively. She received five units of whole blood, fresh frozen plasma, and platelets intra- and postoperatively. The postoperative course was uneventful and she was discharged on seventh postoperative day. The risk of uterine rupture in future pregnancy was explained to the patient and her relatives.

Prostaglandin E 2 production by endogenous secretion of interleukin-1 in decidual cells obtained before and after the labor

Previous reports revealed that interleukin-1(IL-1) was involved in the process of premature labor in the cases with intrauterine infection. However, the roles of the cytokine in normal spontaneous labor remain uncertain. The present studies aimed at determining the involvement of the cytokine in prostaglandin (PG)E 2 production during labor by the third trimester decidual cells. The cells were obtained at the time of normal spontaneous delivery (NVD) and elective cesarean section (ECS). The NVD cells produced significantly more amount of PGE2 than the ECS cells and the both cells responded to the addition of IL-1β to increase PGE 2 production. A specific inhibitor of cyclooxygenase-2 (COX-2), NS398, decreased basal PGE2 production and inhibited the stimulatory effect of IL-1f in a dose dependent manner in NVD cells. The NVD cells secreted more amount of IL-1 fl than the ECS cells and contained more amount of preprocessed 31kD IL-1 fl inside the cells. The addition of recombinant soluble human IL-1 receptor (type I) not only blocked the effect of IL-1β on PG secretion, but significantly reduced the basal production of PGE2 by NVD cells. These results indicate that decidual PG production depends upon COX-2 after the onset of labor. Besides it seems likely that endogenously produced IL-1β may be involved in autocrine fashion in inducing COX-2 after the onset of labor.

Lack of evidence for a circadian rhythm of IGFBP‐1 in the mother and fetus during labour

To determine whether the circadian rhythm of circulating levels of insulin-like growth factor binding protein-1 (IGFBP-1) is evident at the time of delivery. Prospective observational study in six pregnant women and cross-sectional study in 65 women at the time of delivery. Six pregnant women sampled over a period of 24 hours, 23 women sampled at the time of elective caesarean section, and 42 women sampled at the time of vaginal delivery. In the women sampled serially over a 24 hour period there was an obvious circadian rhythm of IGFBP-1 with a peak between 01.00 and 09.00 hours. In the women sampled at the time of delivery there was no evidence for any relationship between the time of delivery and maternal or fetal levels of IGFBP-1. The circadian rhythm of IGFBP-1 is not observed in women in labour. Therefore, the time of day is not an important confounding variable in studies on IGFBP-1 levels at the time of normal delivery.