Abstract-We consider a basic cache network, in which a single server is connected to multiple users via a shared bottleneck link. The server has a database of files (content). Each user has an isolated memory that can be used to cache content in a prefetching phase. In a following delivery phase, each user requests a file from the database, and the server needs to deliver users' demands as efficiently as possible by taking into account their cache contents. We focus on an important and commonly used class of prefetching schemes, where the caches are filled with uncoded data. We provide the exact characterization of the rate-memory tradeoff for this problem, by deriving both the minimum average rate (for a uniform file popularity) and the minimum peak rate required on the bottleneck link for a given cache size available at each user. In particular, we propose a novel caching scheme, which strictly improves the state of the art by exploiting commonality among user demands. We then demonstrate the exact optimality of our proposed scheme through a matching converse, by dividing the set of all demands into types, and showing that the placement phase in the proposed caching scheme is universally optimal for all types. Using these techniques, we also fully characterize the rate-memory tradeoff for a decentralized setting, in which users fill out their cache content without any coordination.

Abstract-We consider a basic cache network, in which a single server is connected to multiple users via a shared bottleneck link. The server has a database of files (content). Each user has an isolated memory that can be used to cache content in a prefetching phase. In a following delivery phase, each user requests a file from the database, and the server needs to deliver users' demands as efficiently as possible by taking into account their cache contents. We focus on an important and commonly used class of prefetching schemes, where the caches are filled with uncoded data. We provide the exact characterization of the rate-memory tradeoff for this problem, by deriving both the minimum average rate (for a uniform file popularity) and the minimum peak rate required on the bottleneck link for a given cache size available at each user. In particular, we propose a novel caching scheme, which strictly improves the state of the art by exploiting commonality among user demands. We then demonstrate the exact optimality of our proposed scheme through a matching converse, by dividing the set of all demands into types, and showing that the placement phase in the proposed caching scheme is universally optimal for all types. Using these techniques, we also fully characterize the rate-memory tradeoff for a decentralized setting, in which users fill out their cache content without any coordination.

No abstract

We consider a basic caching system, where a single server with a database of N files (e.g. movies) is connected to a set of K users through a shared bottleneck link. Each user has a local cache memory with a size of M files. The system operates in two phases: a placement phase, where each cache memory is populated up to its size from the database, and a following delivery phase, where each user requests a file from the database, and the server is responsible for delivering the requested contents. The objective is to design the two phases to minimize the load (peak or average) of the bottleneck link. We characterize the rate-memory tradeoff of the above caching system within a factor of 2.00884 for both the peak rate and the average rate (under uniform file popularity), where the best proved characterization in the current literature gives a factor of 4 and 4.7 respectively. Moreover, in the practically important case where the number of files (N ) is large, we exactly characterize the tradeoff for systems with no more than 5 users, and characterize the tradeoff within a factor of 2 otherwise. We establish these results by developing novel information theoretic outer-bounds for the caching problem, which improves the state of the art and gives tight characterization in various cases. I. INTRODUCTIONCaching is a common strategy to mitigate heavy peak-time communication load in a distributed network, via duplicating parts of the content in memories distributed across the network during off-peak times. In other words, caching allows us to trade distributed memory in the network for communication load reduction. Characterizing this fundamental rate-memory tradeoff is of great practical interest, and has been a research subject for several decades. For single-cache networks, the ratememory tradeoff has been characterized for various scenarios in 80th [1]. However, those techniques were found insufficient to tackle the multiple-cache cases. There has been a surge of recent results in information theory that aim at formalizing and characterizing such rate-memory tradeoff in cache networks [2]- [13]. In particular, the peak rate vs. memory tradeoff was formulated and characterized within a factor of 12 in a basic cache network with a shared bottleneck link [2]. This result has been extended to many scenarios, including decentralized caching [3] Essentially, many of these extensions share similar ideas in terms of the achievability and the converse bounds. Therefore, if we can improve the results for the basic bottleneck caching network, the ideas can be used to improve the results in other cases as well.In the literature, various approaches have been proposed for improving the bounds on rate-memory tradeoff for the bottleneck network. Several caching schemes have been proposed in [14]-[21], and converse bounds have also been introduced in [9], [22]-[26]. For the case, where the prefetching is uncoded, the exact rate-memory tradeoff for both peak and average rate (under uniform file popularity) and for both centra...

This paper describes the mechanism and application of an efficient thia zip cyclization that involves a series of intramolecular rearrangements in a cysteine-rich peptide for the synthesis of large end-to-end cyclic peptides. Key functional groups required in this reaction include an N α-cysteine, a thioester, and at least one internal free thiol in a peptide. The zip reaction is initiated by intramolecular transthioesterification through an internal thiol with the thioester. A thiolactone is formed under ring−chain tautomeric equilibrium that favors ring formation in aqueous buffered solution at pH > 7. Successive ring expansions through thiol−thiolactone exchanges in the direction of the amino terminus lead finally to a large Nα-amino thiolactone which then undergoes a spontaneous and irreversible ring contraction through a sequence-independent S to N acyl isomerization to form an end-to-end lactam. The reversible thiolactone exchanges are sequence-dependent, and the rate-determining steps are shown by rate studies on model peptides. The assistance of internal thiols in reducing the ring sizes and hence the entropy of the thiolactone exchanges correlates well with cyclization rates. Zip-assisted end-to-end cyclizations forming 93- and 99-atom rings through a series of small thiolactone intermediates were 60−200-fold faster under strongly denaturing conditions such as 8 M urea than the corresponding unassisted lactamization. The thia zip reaction has been applied successfully to the synthesis of a 31-amino acid cyclic peptide, the naturally occurring cyclopsychotride that shows the antimicrobial activity. In addition, the thia zip reaction also enables the synthesis of an engineered cyclic 33-amino acid animal defensin by replacing the end-to-end disulfide with a lactam, which retains the antimicrobial activities of the native open-chain form.