Probabilistic latency for partial ordering

International audienceOrdering events in a distributed systems consists fundamentally in delaying event delivery. Partial ordering, such as FIFO and causal order, has many practical usages in distributed systems and can be obtained in arbitrarily large and dynamic networks. However, partial orderings imply that messages cannot be sent and delivered as soon as produced. In this paper, we examine the latency induced by such partial orderings. We obtain a probabilistic measure of the moment a message can be delivered according the different characteristics of the distributed system. Having such a measure helps to understand the systems behavior and to design new protocols. For instance, our measure allows us to parametrize a naive, albeit efficient, fault-tolerant causal delivery mechanism. We experimentally validate our approach using Internet-scale production distribution latency including faults

Probabilistic Shaping for Finite Blocklengths: Distribution Matching and Sphere Shaping

In this paper, we provide for the first time a systematic comparison of distribution matching (DM) and sphere shaping (SpSh) algorithms for short blocklength probabilistic amplitude shaping. For asymptotically large blocklengths, constant composition distribution matching (CCDM) is known to generate the target capacity-achieving distribution. As the blocklength decreases, however, the resulting rate loss diminishes the efficiency of CCDM. We claim that for such short blocklengths and over the additive white Gaussian channel (AWGN), the objective of shaping should be reformulated as obtaining the most energy-efficient signal space for a given rate (rather than matching distributions). In light of this interpretation, multiset-partition DM (MPDM), enumerative sphere shaping (ESS) and shell mapping (SM), are reviewed as energy-efficient shaping techniques. Numerical results show that MPDM and SpSh have smaller rate losses than CCDM. SpSh--whose sole objective is to maximize the energy efficiency--is shown to have the minimum rate loss amongst all. We provide simulation results of the end-to-end decoding performance showing that up to 1 dB improvement in power efficiency over uniform signaling can be obtained with MPDM and SpSh at blocklengths around 200. Finally, we present a discussion on the complexity of these algorithms from the perspective of latency, storage and computations.Comment: 18 pages, 10 figure

Reliable Messaging to Millions of Users with MigratoryData

Web-based notification services are used by a large range of businesses to selectively distribute live updates to customers, following the publish/subscribe (pub/sub) model. Typical deployments can involve millions of subscribers expecting ordering and delivery guarantees together with low latencies. Notification services must be vertically and horizontally scalable, and adopt replication to provide a reliable service. We report our experience building and operating MigratoryData, a highly-scalable notification service. We discuss the typical requirements of MigratoryData customers, and describe the architecture and design of the service, focusing on scalability and fault tolerance. Our evaluation demonstrates the ability of MigratoryData to handle millions of concurrent connections and support a reliable notification service despite server failures and network disconnections