Generating Good Degree Distributions for Sparse Parity Check Codes using Oracles

Fast forward error correction codes are becoming an important component in bulk content delivery. They fit in naturally with multicast scenarios as a way to deal with losses and are now seeing use in peer to peer networks as a basis for distributing load. In particular, new irregular sparse parity check codes have been developed with provable average linear time performance, a significant improvement over previous codes. In this paper, we present a new heuristic for generating codes with similar performance based on observing a server with an oracle for client state. This heuristic is easy to implement and provides further intuition into the need for an irregular heavy tailed distribution.

Small-World Internet Topologies: Possible Causes and Implications on Scalability of End-System Multicast

Recent work has shown the prevalence of small-world phenomena [28] in many networks. Small-world graphs exhibit a high degree of clustering, yet have typically short path lengths between arbitrary vertices. Internet AS-level graphs have been shown to exhibit small-world behaviors [9]. In this paper, we show that both Internet AS-level and router-level graphs exhibit small-world behavior. We attribute such behavior to two possible causes���namely the high variability of vertex degree distributions (which were found to follow approximately a power law [15]) and the preference of vertices to have local connections. We show that both factors contribute with different relative degrees to the small-world behavior of AS-level and router-level topologies. Our findings underscore the inefficacy of the Barabasi-Albert model [6] in explaining the growth process of the Internet, and provide a basis for more promising approaches to the development of Internet topology generators. We present such a generator and show the resemblance of the synthetic graphs it generates to real Internet AS-level and router-level graphs. Using these graphs, we have examined how small-world behaviors affect the scalability of end-system multicast. Our findings indicate that lower variability of vertex degree and stronger preference for local connectivity in small-world graphs results in slower network neighborhood expansion, and in longer average path length between two arbitrary vertices, which in turn results in better scaling of end system multicast.

Mistreatment in Distributed Caching Groups: Causes and Implications

Although cooperation generally increases the amount of resources available to a community of nodes, thus improving individual and collective performance, it also allows for the appearance of potential mistreatment problems through the exposition of one node’s resources to others. We study such concerns by considering a group of independent, rational, self-aware nodes that cooperate using on-line caching algorithms, where the exposed resource is the storage of each node. Motivated by content networking applications – including web caching, CDNs, and P2P – this paper extends our previous work on the off-line version of the problem, which was limited to object replication and was conducted under a game-theoretic framework. We identify and investigate two causes of mistreatment: (1) cache state interactions (due to the cooperative servicing of requests) and (2) the adoption of a common scheme for cache replacement/redirection/admission policies. Using analytic models, numerical solutions of these models, as well as simulation experiments, we show that online cooperation schemes using caching are fairly robust to mistreatment caused by state interactions. When this becomes possible, the interaction through the exchange of miss-streams has to be very intense, making it feasible for the mistreated nodes to detect and react to the exploitation. This robustness ceases to exist when nodes fetch and store objects in response to remote requests, i.e., when they operate as Level-2 caches (or proxies) for other nodes. Regarding mistreatment due to a common scheme, we show that this can easily take place when the “outlier” characteristics of some of the nodes get overlooked. This finding underscores the importance of allowing cooperative caching nodes the flexibility of choosing from a diverse set of schemes to fit the peculiarities of individual nodes. To that end, we outline an emulation-based framework for the development of mistreatment-resilient distributed selfish caching schemes.

Space, Time and Learning in the Hippocampus: How Fine Spatial and Temporal Scales Are Expanded into Population Codes for Behavioral Control

The hippocampus participates in multiple functions, including spatial navigation, adaptive timing, and declarative (notably, episodic) memory. How does it carry out these particular functions? The present article proposes that hippocampal spatial and temporal processing are carried out by parallel circuits within entorhinal cortex, dentate gyrus, and CA3 that are variations of the same circuit design. In particular, interactions between these brain regions transform fine spatial and temporal scales into population codes that are capable of representing the much larger spatial and temporal scales that are needed to control adaptive behaviors. Previous models of adaptively timed learning propose how a spectrum of cells tuned to brief but different delays are combined and modulated by learning to create a population code for controlling goal-oriented behaviors that span hundreds of milliseconds or even seconds. Here it is proposed how projections from entorhinal grid cells can undergo a similar learning process to create hippocampal place cells that can cover a space of many meters that are needed to control navigational behaviors. The suggested homology between spatial and temporal processing may clarify how spatial and temporal information may be integrated into an episodic memory.

Distributed Hypothesis Testing, Attention Shifts and Transmitter Dynatmics During the Self-Organization of Brain Recognition Codes

BP (89-A-1204); Defense Advanced Research Projects Agency (90-0083); National Science Foundation (IRI-90-00530); Air Force Office of Scientific Research (90-0175, 90-0128); Army Research Office (DAAL-03-88-K0088)