In this paper, we investigate the index coding problem in the presence of an eavesdropper. Messages are to be sent from one transmitter to a number of legitimate receivers who have side information about the messages, and share a set of secret keys with the transmitter. We assume perfect secrecy, meaning that the eavesdropper should not be able to retrieve any information about the message set. We study the minimum key lengths for zero-error and perfectly secure index coding problem. On one hand, this problem is a generalization of the index coding problem (and thus a difficult one). On the other hand, it is a generalization of the Shannon's cipher system. We show that a generalization of Shannon's one-time pad strategy is optimal up to a multiplicative constant, meaning that it obtains the entire boundary of the cone formed by looking at the secure rate region from the origin. Finally, we consider relaxation of the perfect secrecy and zero-error constraints to weak secrecy and asymptotically vanishing probability of error, and provide a secure version of the result, obtained by Langberg and Effros, on the equivalence of zero-error and ǫ-error regions in the conventional index coding problem. Index TermsIndex coding, Shannon cipher system, perfect secrecy, common and private keys, zero-error communication.

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The results indicate a significant difference between EA and NSAIDs in cases of both utility and total cost. The findings demonstrate that EA is more cost-effective than NSAIDs, as therefore can be considered as an alternative treatment for CLBP, with reasonable cost-utility.

This paper formulates regularized zero-forcing (RZF) precoders that are both network-and user-centric for the downlink of centralized radio-access networks operating in a cellfree fashion. The transmission to every user involves a distinct subset of access points (APs), and every AP participates in the transmission to a distinct subset of users, hence the moniker subset precoders. These subsets, defined on the basis of the largescale channel gains between users and APs, capture the most relevant signal and interference contributions while disregarding those whose processing is cost-ineffective and whose associated channel estimations would incur unnecessary overheads. With that, subset precoding approaches the performance of networkwide RZF, for the power allocation strategies of interest, while being scalable.

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