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We consider the three-receiver Gaussian multiple-input multiple-output broadcast channel with an arbitrary number of antennas at the transmitter and the receivers. We investigate the degrees-of-freedom (DoF) region of the channel when each receiver requests a private message, and may know some of the messages requested by the other receivers as receiver message side information (RMSI). We establish the DoF region of the channel for all 16 possible non-isomorphic RMSI configurations by deriving tight inner and outer bounds on the region. To derive the inner bounds, we first propose a scheme for each RMSI configuration, which exploits both the null space and the side information of the receivers. We then use these schemes in conjunction with time sharing for 15 RMSI configurations, and with time sharing and two-symbol extension for the remaining one. To derive the outer bounds, we construct enhanced versions of the channel for each RMSI configuration, and upper bound their DoF region. After establishing the DoF region, in the case where all the nodes have the same number of antennas, we introduce some common properties of the DoF region, and the capacity region of the index coding problem. [ABSTRACT FROM PUBLISHER]

Index coding studies multiterminal source-coding problems where a set of receivers are required to decode multiple (possibly different) messages from a common broadcast, and they each know some messages a priori. In this paper, at the receiver end, we consider a special setting where each receiver knows only one message a priori, and each message is known to only one receiver. At the broadcasting end, we consider a generalized setting where there could be multiple senders, and each sender knows a subset of the messages. The senders collaborate to transmit an index code. This paper looks at minimizing the number of total coded bits the senders are required to transmit. When there is only one sender, we propose a pruning algorithm to find a lower bound on the optimal (i.e., the shortest) index codelength, and show that it is achievable by linear index codes. When there are two or more senders, we propose an appending technique to be used in conjunction with the pruning technique to give a lower bound on the optimal index codelength; we also derive an upper bound based on cyclic codes. While the two bounds do not match in general, for the special case where no two distinct senders know any message in common, the bounds match, giving the optimal index codelength. The results are expressed in terms of strongly connected components in directed graphs that represent the index-coding problems. [ABSTRACT FROM AUTHOR]

This paper investigates the capacity region of the three-receiver AWGN broadcast channel where the receivers: 1) have private-message requests and 2) may know some of the messages requested by other receivers as side information. We first classify all 64 possible side information configurations into eight groups, each consisting of eight members. We next construct transmission schemes, and derive new inner and outer bounds for the groups. This establishes the capacity region for 52 out of 64 possible side information configurations. For six groups (i.e., groups 1, 2, 3, 5, 6, and 8 in our terminology), we establish the capacity region for all their members, and show that it tightens both the best-known inner and outer bounds. For group 4, our inner and outer bounds tighten the best-known inner bound and/or outer bound for all the group members. Moreover, our bounds coincide at certain regions, which can be characterized by two thresholds. For group 7, our inner and outer bounds coincide for four members, and thereby establishing the capacity region. For the remaining four members, our bounds tighten both the best-known inner and outer bounds. [ABSTRACT FROM PUBLISHER]

This letter investigates the role of index coding in the capacity of AWGN broadcast channels with receiver message side information. We first show that index coding is unnecessary where there are two receivers; multiplexing coding and superposition coding are sufficient to achieve the capacity region. We next show that, for more than two receivers, multiplexing coding and superposition coding alone can be suboptimal. We give an example where these two coding schemes alone cannot achieve the capacity region, but adding index coding can. This demonstrates that, in contrast to the two-receiver case, multiplexing coding cannot fulfill the function of index coding where there are three or more receivers. [ABSTRACT FROM PUBLISHER]

This paper compares the partial-decode-forward and the complete-decode-forward coding strategies for the half-duplex Gaussian single-relay channel. We analytically show that the rate achievable by partial-decode-forward outperforms that of the more straightforward complete-decode-forward by at most 12.5%. Furthermore, in the following asymptotic cases, the gap between the partial-decode-forward and the complete-decode-forward rates diminishes: (i) when the relay is close to the source, (ii) when the relay is close to the destination, and (iii) when the SNR is low. In addition, when the SNR increases, this gap, when normalized to the complete-decode-forward rate, also diminishes. Consequently, significant performance improvements are not achieved by optimizing the fraction of data the relay should decode and forward, over simply decoding the entire source message. [ABSTRACT FROM AUTHOR]

The L-user additive white Gaussian noise multiway relay channel is investigated, where L users exchange information at the same rate through a single relay. A new achievable rate region, based on the functional-decode-forward coding strategy, is derived. For the case where there are three or more users, and all nodes transmit at the same power, the capacity is obtained. For the case where the relay power scales with the number of users, it is shown that both compress-forward and functional-decode-forward achieve rates within a constant number of bits of the capacity at all SNR levels; in addition, functional-decode-forward outperforms compress-forward and complete-decode-forward at high SNR levels. [ABSTRACT FROM AUTHOR]

We study the half-duplex multiple-relay channel (HD-MRC) where every node can either transmit or listen but cannot do both at the same time. We obtain a capacity upper bound based on a max-flow min-cut argument and achievable transmission rates based on the decode-forward (DF) coding strategy, for both the discrete memoryless HD-MRC and the phase-fading HD-MRC. We discover that both the upper bound and the achievable rates are functions of the transmit/listen state (a description of which nodes transmit and which receive). More precisely, they are functions of the time fraction of the different states, which we term a schedule. We formulate the optimal scheduling problem to find an optimal schedule that maximizes the DF rate. The optimal scheduling problem turns out to be a maximin optimization, for which we propose an algorithmic solution. We demonstrate our approach on a four-node multiple-relay channel, obtaining closed-form solutions in certain scenarios. Furthermore, we show that for the received signal-to-noise ratio degraded phase-fading HD-MRC, the optimal scheduling problem can be simplified to a max optimization. [ABSTRACT FROM AUTHOR]

The multiway relay channel is a multicast network where L users exchange data through a relay. In this paper, the capacity region of a class of multiway relay channels is derived, where the channel inputs and outputs take values over finite fields. The cut-set upper bound to the capacity region is derived and is shown to be achievable by our proposed functional-decode-forward coding strategy. More specifically, for the general case where the users can transmit at possibly different rates, functional-decode-forward, combined with rate splitting and joint source-channel decoding, is proved to achieve the capacity region; while for the case where all users transmit at a common rate, rate splitting and joint source-channel decoding are not required to achieve the capacity. That the capacity-achieving coding strategies do not utilize the users' received signals in the users' encoding functions implies that feedback does not increase the capacity region of this class of multiway relay channels. [ABSTRACT FROM PUBLISHER]

The multiple-access channel with feedback and correlated sources (MACFCS) models a sensor network in which sensors collect and transmit correlated data to a common sink. We present four achievable rate regions and a capacity outer bound for the MACFCS. For the first achievable region, we construct a decode-forward based coding strategy. The sources first exchange their data, and then cooperate to send full information to the destination. We term this strategy full decoding at sources with decode-forward IFDS-DF). For two of the other achievable regions, we first perform Slepian-Wolf coding to remove the correlation among the source data. This is followed by either i) a compress-forward based coding strategy for the multiple-access channel with feedback, or ii) an existing coding strategy for the multiple-access channel. We also find another achievable region using a multihop coding strategy, which only uses point-to-point coding (no cooperation). From numerical computations, we see that different strategies perform better under certain source correlation structures and network topologies. More specifically, FDS-DF approaches the capacity when i) the inter-source distance decreases, or ii) the correlation among the sources gets higher. Furthermore, the cooperative coding strategies considered support larger achievable rate regions than the noncooperative multihop strategy. [ABSTRACT FROM AUTHOR]

This paper considers the two-way relay channel (TWRC) where two users communicate via a relay. For the restricted TWRC where the uplink from the users to the relay is any deterministic function and the downlink from the relay to the users is any arbitrary channel, the capacity region is obtained. The TWRC considered is restricted in the sense that each user can only transmit a function of its message. [ABSTRACT FROM PUBLISHER]