Capacity of 1-to-K Broadcast Packet Erasure Channels with Channel Output Feedback

This paper focuses on the 1-to-K broadcast packet erasure channel (PEC), which is a generalization of the broadcast binary erasure channel from the binary symbol to that of arbitrary finite fields GF(q) with sufficiently large q. We consider the setting in which the source node has instant feedback of the channel outputs of the K receivers after each transmission. Such a setting directly models network coded packet transmission in the downlink direction with integrated feedback mechanisms (such as Automatic Repeat reQuest (ARQ)). The main results of this paper are: (i) The capacity region for general 1-to-3 broadcast PECs, and (ii) The capacity region for two classes of 1-to-K broadcast PECs: the symmetric PECs, and the spatially independent PECs with one-sided fairness constraints. This paper also develops (iii) A pair of outer and inner bounds of the capacity region for arbitrary 1-to-K broadcast PECs, which can be evaluated by any linear programming solver. For most practical scenarios, the outer and inner bounds meet and thus jointly characterize the capacity.Comment: 8 pages, 2 figures. Published in Allerton 2010. The journal version of this work was submitted to IEEE Trans IT in May, 201

Secret Communication over Broadcast Erasure Channels with State-feedback

We consider a 1-to-$K$ communication scenario, where a source transmits private messages to $K$ receivers through a broadcast erasure channel, and the receivers feed back strictly causally and publicly their channel states after each transmission. We explore the achievable rate region when we require that the message to each receiver remains secret - in the information theoretical sense - from all the other receivers. We characterize the capacity of secure communication in all the cases where the capacity of the 1-to-$K$ communication scenario without the requirement of security is known. As a special case, we characterize the secret-message capacity of a single receiver point-to-point erasure channel with public state-feedback in the presence of a passive eavesdropper. We find that in all cases where we have an exact characterization, we can achieve the capacity by using linear complexity two-phase schemes: in the first phase we create appropriate secret keys, and in the second phase we use them to encrypt each message. We find that the amount of key we need is smaller than the size of the message, and equal to the amount of encrypted message the potential eavesdroppers jointly collect. Moreover, we prove that a dishonest receiver that provides deceptive feedback cannot diminish the rate experienced by the honest receivers. We also develop a converse proof which reflects the two-phase structure of our achievability scheme. As a side result, our technique leads to a new outer bound proof for the non-secure communication problem

Content Delivery in Erasure Broadcast Channels with Cache and Feedback

We study a content delivery problem in a K-user erasure broadcast channel such that a content providing server wishes to deliver requested files to users, each equipped with a cache of a finite memory. Assuming that the transmitter has state feedback and user caches can be filled during off-peak hours reliably by the decentralized content placement, we characterize the achievable rate region as a function of the memory sizes and the erasure probabilities. The proposed delivery scheme, based on the broadcasting scheme by Wang and Gatzianas et al., exploits the receiver side information established during the placement phase. Our results can be extended to centralized content placement as well as multi-antenna broadcast channels with state feedback.Comment: 29 pages, 7 figures. A short version has been submitted to ISIT 201