English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We resolve the question of optimality for a well-studied packetizedimplementation of random linear network coding, called PNC. In PNC, in contrastto the classical memoryless setting, nodes store received information in memoryto later produce coded packets that reflect this information. PNC is known toachieve order optimal stopping times for the many-to-all multicast problem inmany settings.  We give a reduction that captures exactly how PNC and other network codingprotocols use the memory of the nodes. More precisely, we show that any suchprotocol implementation induces a transformation which maps an execution of theprotocol to an instance of the classical memoryless setting. This allows us toprove that, for any (non-adaptive dynamic) network, PNC converges with highprobability in optimal time. In other words, it stops at exactly the first timein which in hindsight it was possible to route information from the sources toeach receiver individually.  Our technique also applies to variants of PNC, in which each node uses only afinite buffer. We show that, even in this setting, PNC stops exactly within thetime in which in hindsight it was possible to route packets given the memoryconstraint, i.e., that the memory used at each node never exceeds its buffersize. This shows that PNC, even without any feedback or explicit memorymanagement, allows to keep minimal buffer sizes while maintaining its capacityachieving performance.

Optimality of Network Coding in Packet Networks