Private information retrieval scheme for coded data storage is considered in this paper. We focus on the case where the size of each data record is large and hence only the download cost (but not the upload cost for transmitting retrieval queries) is of interest. We prove that the tradeoff between storage cost and retrieval/download cost depends on the number of data records in the system. We also propose a fairly general class of linear storage codes and retrieval schemes and derive conditions under which our retrieval schemes are error-free and private. Tradeoffs between the storage cost and retrieval costs are also obtained. Finally, we consider special cases when the underlying storage code is based on an MDS code. Using our proposed method, we show that a randomly generated retrieval scheme is indeed very likely to be private and error-free.
Abstract-This paper proposes two novel and practical designs of angle diversity receivers to achieve multiple-input-multipleoutput (MIMO) capacity for indoor visible light communications (VLC). Both designs are easy to be constructed and suitable for small mobile devices. By using light emitting diodes for both illumination and data transmission, our receiver designs consist of multiple photodetectors (PDs) which are oriented with different inclination angles to achieve high-rank MIMO channels and can be closely packed without the requirement of spatial separation. Due to the orientations of the PDs, the proposed receiver designs are named pyramid receiver (PR) and hemispheric receiver (HR). In a PR, the normal vectors of PDs are chosen the same as the normal vectors of the triangle faces of a pyramid with equilateral N -gon base. On the other hand, the idea of HR is to evenly distribute the PDs on a hemisphere. Through analytical investigation, simulations and experiments, the channel capacity and bit-error-rate (BER) performance under various settings are presented to show that our receiver designs are practical and promising for enabling VLC-MIMO. In comparison to induced link-blocked receiver, our designs do not require any hardware adjustment at the receiver from location to location so that they can support user mobility. Besides, their channel capacities and BER performance are quite close to that of link-blocked receiver. Meanwhile, they substantially outperform spatiallyseparated receiver. This study reveals that using angle diversity to build VLC-MIMO system is very promising.Index Terms-Visible light communications, multiple-inputmultiple-output (MIMO), angle diversity, pyramid receiver, hemispheric receiver.
Abstract-Fano's inequality relates the error probability of guessing a finitely-valued random variable given another random variable and the conditional entropy of given . It is not necessarily tight when the marginal distribution of is fixed. This paper gives a tight upper bound on the conditional entropy of given in terms of the error probability and the marginal distribution of . A new lower bound on the conditional entropy for countably infinite alphabets is also found. The relationship between the reliability criteria of vanishing error probability and vanishing conditional entropy is also discussed. A strengthened form of the Schur-concavity of entropy which holds for finite or countably infinite random variables is given.
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