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

A Novel Transmission Scheme for the KK-user Broadcast Channel with Delayed CSIT

The state-dependent $K$-user memoryless Broadcast Channel~(BC) with state feedback is investigated. We propose a novel transmission scheme and derive its corresponding achievable rate region, which, compared to some general schemes that deal with feedback, has the advantage of being relatively simple and thus is easy to evaluate. In particular, it is shown that the capacity region of the symmetric erasure BC with an arbitrary input alphabet size is achievable with the proposed scheme. For the fading Gaussian BC, we derive a symmetric achievable rate as a function of the signal-to-noise ratio~(SNR) and a small set of parameters. Besides achieving the optimal degrees of freedom at high SNR, the proposed scheme is shown, through numerical results, to outperform existing schemes from the literature in the finite SNR regime.Comment: 30 pages, 3 figures, submitted to IEEE Transactions on Wireless Communications (revised version

Capacities of erasure networks

textWe have investigated, in various multiple senses, the “capacity” of several models of erasure networks. The defining characteristic of a memoryless erasure network is that each channel between any two nodes is an independent erasure channel. The models that we explore differ in the absence or presence of interference at either the transmitters, the receivers, or both; and in the availability of feedback at the transmitters. The crux of this work involves the investigation and analysis of several different performance measures for these networks: traditional information capacity (including multicast capacity and feeback capacity), secrecy capacity, and transport capacity.Electrical and Computer Engineerin