We propose a novel transmission scheme for ultra-reliable multi-hop multiple-antenna communication where relays perform only universal linear operations on the received signals. In particular, the operations are channel-oblivious, and no detection takes place in intermediate relaying nodes. The processing at each relay may be viewed as a concatenation of a dimension-reduction operation, i.e., a universal combining, and orthogonal space-time block coding, i.e., a universal transmission operation. It is demonstrated that the developed transmission-combining relaying technique guarantees reliable communication in a very strong sense: so long as all relay-to-relay links have a non-vanishing capacity, reliable communication is possible. The proposed schemes are derived by establishing a certain operational equivalence relationship between the true channel and an associated multiple-input single-output channel.

We consider a line network of nodes connected by additive white Gaussian noise channels and equipped with local feedback. We study the velocity at which information spreads over this network. For the transmission of a data packet, we derive an explicit positive lower bound on the velocity for any packet size. Furthermore, we consider streaming, that is, transmission of data packets that is generated at a given average arrival rate. We show that a positive velocity exists as long as the arrival rate is below the individual Gaussian channel capacity and provide an explicit lower bound. Our analysis involves applying pulse-amplitude modulation to the data (successively in the streaming case) and using linear mean-squared error estimation at the network nodes. Due to the analog-linear nature of the scheme, the results extend to any additive noise. For general noise, we derive exponential error-probability bounds. Moreover, for (sub-)Gaussian noise, we show doubly-exponential behavior, which reduces to the celebrated Schalkwijk-Kailath scheme when considering a single node. By viewing the constellation as an “analog source”, we also provide bounds on the exponential decay of the mean-squared error of source transmission over the network.

Many emerging multimedia streaming applications involve multiple users communicating under strict latency constraints. In this paper we study streaming codes for a network involving two source nodes, one relay node and a destination node. In this paper’s setting, each source node transmits a stream of messages, through the relay, to a destination, who is required to decode the messages under a strict delay constraint. For the case of a single source node, a class of streaming codes has been proposed by Fong et al., using the concept of delay-spectrum. The current paper presents a novel framework, which constructs streaming codes for a relayed multi-user setting by sequentially constructing the codes for each link. This requires a characterization of the set of all achievable delay spectra for a given rate, blocklength and number of erasures, beyond the specific choice considered by Fong et al. This characterization is presented in the paper for systematic codes. Using this novel framework, the first proposed scheme involves greedily selecting the rate on the link from relay to destination and using properties of the delay-spectrum to find feasible streaming codes that satisfy the required delay constraints. A closed form expression for the achievable rate region is provided, and conditions for when the proposed scheme is optimal are established by a natural outer bound. The second proposed scheme builds upon this approach, but uses a numerical optimization-based approach to improve the achievable rate region over the first scheme. Experimental results show that the proposed schemes achieve significant improvements over baseline schemes based on single-user codes.

This paper investigates adaptive streaming codes over a three-node relayed network. In this setting, a source node transmits a sequence of message packets to a destination with help of a relay. The source-to-relay and relay-to-destination links are unreliable and introduce at most$N_{1}$and$N_{2}$packet erasures, respectively. The destination node must recover each message packet within a strict delay constraint$T$. The paper presents a new construction of streaming codes for all feasible parameters$\{N_{1}, N_{2}, T\}$. Our work improves upon the construction in Fong et al. by adapting the relaying strategy based on the erasure patterns from source to relay. Specifically, the code employs the notion of symbol estimates, which allows the relay to forward information about symbols before it can decode that symbol, and variable-rate encoding, which decreases the rate used to encode a packet as more erasures affect that packet. The codes proposed in this paper achieve rates higher than the ones proposed by Fong et al. whenever$N_{2} > N_{1}$, and achieve the same rate when$N_{2} \leq N_{1}$, in which case the rate is optimal. The paper also presents an upper bound on the achievable rate that takes into account erasures in both links in order to bound the rate in the second link. The upper bound is shown to be tighter than a trivial bound that considers only the erasures in the second link.

This paper proposes a data-driven architecture for zero-delay lossy source coding with side information (i.e., Wyner-Ziv coding) for sources with memory. The overall architecture involves designing suitable filters at the encoder and the decoder and performing fixed-rate scalar quantization followed by one-dimensional binning of quantization indices. Unlike previous work, which uses an exhaustive search to optimize the system parameters, this paper proposes a lower-complexity data-driven method that does not require a priori knowledge of source and side information statistics. The main ingredients of the proposed approach include modeling the quantization process by an additive quantization noise process, modeling the modulo operation by a continuous approximation, and approximating the decoding process by a softmin function, which makes the system amenable to training using stochastic gradient descent. Experimental results on Gauss-Markov sources with different memory orders demonstrate that our proposed system can match the performance of systems optimized using an exhaustive search.

We consider the problem of in-order packet transmission over a cascade of packet-erasure links with acknowledgment (ACK) signals, interconnected by relays. We treat first the case of transmitting a single packet, in which ACKs are unnecessary, over links with independent identically distributed erasures. For this case, we derive tight upper and lower bounds on the probability of arrive failure within an allowed end-to-end communication delay over a given number of links. When the number of links is commensurate with the allowed delay, we determine the maximal ratio between the two—coined information velocity—for which the arrive-failure probability decays to zero; we further derive bounds on the arrive-failure probability when the ratio is below the information velocity, determine the exponential arrive-failure decay rate, and extend the treatment to links with different erasure probabilities. We then elevate all these results for a stream of packets with independent geometrically distributed interarrival times, and prove that the information velocity and the exponential decay rate remain the same for any stationary ergodic arrival process and for deterministic interarrival times. We demonstrate the significance of the derived fundamental limits—the information velocity and the arrive-failure exponential decay rate—by comparing them to simulation results.

This paper investigates low-latency adaptive streaming codes for a three-node relay network. A source node transmits a sequence of source packets (messages) to the destination through a relay node. We focus on a particular case where the link connecting the source and relay nodes is almost reliable, but the link connecting the relay to the destination is not. The relay node can observe the erasure pattern that has occurred in the transmission between the source node and itself and adapt its relaying strategy based on that observation. Every source packet must be perfectly recovered by the destination with a strict delay T, as long as the number of erasures in the relay-to-destination link lies below some design parameter. We then characterize capacity as a function of such design parameter. The achievability scheme employs two different relaying strategies, based on whether an erasure has or has not occurred in the link from source to relay. The converse is proven by analyzing a periodic erasure pattern and lower bounding the minimum redundancy across channel packets. We show that the achievable rate can be improved compared to non-adaptive schemes previously proposed, indicating that exploiting the knowledge of the erasure pattern by the relay node is essential in achieving capacity.

This paper studies low-latency streaming codes for the multi-hop network. The source transmits a sequence of messages to a destination through a chain of relays, and requires the destination to reconstruct each message by its deadline. We assume that each communication link is subjected to a certain maximum number of packet erasures. The case of a single relay (a three-node network) was considered in Fong et al. (2020). A coding scheme known as symbol-wise decode and forward was proposed. In the present work, we propose an alternative scheme that is different from Fong et al. (2020) and still achieves the same rate as in Fong et al. (2020) for the one hop case as the field-size goes to infinity. Furthermore, our proposed scheme naturally generalizes to the case of multiple-relay nodes yielding new achievable rates for this setting. The main difference with Fong et al. (2020) is that our proposed scheme exploits the ability of the relay nodes to adapt the transmission based on the erasures on the previous link. Hence, we refer to our scheme as “state-dependent” and contrast it with the scheme in Fong et al. (2020) that is state-independent. Our scheme requires the relay nodes to append a header to the transmitted packets, and we show that the size of the header does not depend on the field-size of the code. We also derive an upper bound on the maximal streaming rate achievable over a network with an arbitrary number of relays. We show that this upper bound matches our achievable rate in the special case when the maximal number of erasures on the first link is greater than or equal to the maximal number of erasures on each of the following links, and the field size goes to infinity.

This work addresses general multiple-input multiple-output systems and develops combined diversity transmission and combining schemes that achieve rate one and full diversity with reduced decoding complexity, while being universal in the sense that the operations performed at both transmission ends are channel independent. Such schemes may be useful in a scenario where a multiple-antenna source node communicates with the cloud via a multiple-antenna "dumb relay" that forwards the received vector over a rate-constrained digital front-haul link or serves as relay performing an amplify-forward operation over the air. The proposed schemes are derived by establishing an operational equivalence relation between the true channel and an associated multiple-input single-output channel.

Applications where multiple users communicate with a common server and desire low latency are common and increasing. This paper studies a network with two source nodes, one relay node and a destination node, where each source nodes wishes to transmit a sequence of messages, through the relay, to the destination, who is required to decode the messages with a strict delay constraint$T$. The network with a single source node has been studied in [1]. We start by introducing two important tools: the delay spectrum, which generalizes delay-constrained point-to-point transmission, and concatenation, which, similar to time sharing, allows combinations of different codes in order to achieve a desired regime of operation. Using these tools, we are able to generalize the two schemes previously presented in [1], and propose a novel scheme which allows us to achieve optimal rates under a set of well-defined conditions. Such novel scheme is further improved in order to achieve higher rates in the scenarios where the conditions for optimality are not met.

We study the problem of transmitting a sequence of messages (streaming messages) through a multi-link, multi-hop packet erasure network. Each message must be reconstructed in-order and under a strict delay constraint. Special cases of our setting with a single link on each hop have been studied recently - the case of a single relay-node, is studied in Fong et al [1]; the case of multiple relays, is studied in Domanovitz et al [2]. As our main result, we propose an achievable rate expression that reduces to previously known results when specialized to their respective settings. Our proposed scheme is based on the idea of concatenating single-link codes from [2] in a judicious manner to achieve the required delay constraints. We propose a systematic approach based on convex optimization to maximize the achievable rate in our framework.

In this paper, we investigate streaming codes over a three-node relay network. Source node transmits a sequence of message packets to the destination via a relay. Source-to-relay and relay-to-destination links are unreliable and introduce at most N1and N2packet erasures, respectively. Destination needs to recover each message packet with a strict decoding delay constraint of T time slots. We propose streaming codes under this setting for all feasible parameters $\{N_{1},\ N_{2},\ T\}$. Relay naturally observes erasure patterns occurring in the source-to-relay link. In our code construction, we employ a channel-state-dependent relaying strategy, which rely on these observations. In a recent work, Fong et al. provide streaming codes featuring channel-state-independent relaying strategies, for all feasible parameters $\{N_{1},\ N_{2},\ T\}$. Our schemes offer a strict rate improvement over the schemes proposed by Fong et al., whenever $N_{1}\lt N_{2}$.

A typical path over the internet is composed of multiple hops. When considering the transmission of a sequence of messages (streaming messages) through packet erasure channel over a three-node network, it has been shown that taking into account the erasure pattern of each segment can result in improved performance compared to treating the channel as a point-to-point link. Since rarely there is only a single relay between the sender and the destination, it calls for trying to extend this scheme to more than a single relay. In this paper, we first extend the upper bound on the rate of transmission of a sequence of messages for any number of relays. We further suggest an achievable adaptive scheme that is shown to achieve the upper bound up to the size of an additional header that is required to allow each receiver to meet the delay constraints.

Integer-forcing source coding has been proposed as a low-complexity method for compression of distributed correlated Gaussian sources. In this scheme, each encoder quantizes its observation using the same fine lattice and reduces the result modulo a coarse lattice. Rather than directly recovering the individual quantized signals, the decoder first recovers a full-rank set of judiciously chosen integer linear combinations of the quantized signals, and then inverts it. It has been observed that the method works very well for “most” but not all source covariance matrices. The present work quantifies the measure of bad covariance matrices by studying the probability that integer-forcing source coding fails as a function of the allocated rate, where the probability is with respect to a random orthonormal transformation that is applied to the sources prior to quantization. For the important case where the signals to be compressed correspond to the antenna inputs of relays in an i.i.d. Rayleigh fading environment, this orthonormal transformation can be viewed as being performed by nature. The scheme is also studied in the context of a non-distributed system. Here, the goal is to arrive at a universal, yet practical, compression method using equal-rate quantizers with provable performance guarantees. The scheme is universal in the sense that the covariance matrix need only be learned at the decoder but not at the encoder. The goal is accomplished by replacing the random orthonormal transformation by transformations corresponding to number-theoretic space-time codes.

Communication over the i.i.d. Rayleigh slow-fading MAC is considered, where all terminals are equipped with a single antenna. Further, a communication protocol is considered where all users transmit at (just below) the symmetric capacity (per user) of the channel, a rate which is fed back (dictated) to the users by the base station. Tight bounds are established on the distribution of the rate attained by the protocol. In particular, these bounds characterize the probability that the dominant face of the MAC capacity region contains a symmetric rate point, i.e., that the considered protocol strictly attains the sum capacity of the channel. The analysis provides a non-asymptotic counterpart to the diversity-multiplexing tradeoff of the multiple access channel. We then extend this analysis to general multiple-input multiple-output MAC and finally, a practical scheme based on integer-forcing and space-time precoding is shown to be an effective coding architecture for this communication scenario.

The maximal correlation coefficient is a well-established generalization of the Pearson correlation coefficient for measuring non-linear dependence between random variables. It is appealing from a theoretical standpoint, satisfying Rényi's axioms for measures of dependence. It is also attractive from a computational point of view due to the celebrated alternating conditional expectation algorithm, allowing to compute its empirical version directly from observed data. Nevertheless, from the outset, it was recognized that the maximal correlation coefficient suffers from some fundamental deficiencies, limiting its usefulness as an indicator of estimation quality. Another well-known measure of dependence is the correlation ratio but it too suffers from some drawbacks. Specifically, the maximal correlation coefficient equals one too easily whereas the correlation ratio equals zero too easily. The present work recounts some attempts that have been made in the past to alter the definition of the maximal correlation coefficient in order to overcome its weaknesses and then proceeds to suggest a natural variant of the maximal correlation coefficient. The proposed dependence measure at the same time resolves the major weakness of the correlation ratio measure and may be viewed as a bridge between the two classical measures.

In this paper, we consider transmitting a sequence of messages (a streaming source) over a packet erasure channel, where every source message must be recovered perfectly at the destination subject to a fixed decoding delay. Recently, the capacity of such a channel was established. However, the codes shown to achieve the capacity are either non-explicit constructions (proven to exist) or explicit constructions requiring large field size that scales exponentially with the delay. This work presents an explicit rate-optimal construction for all channel and delay parameters over a field size that scales only quadratically with the delay.

Receiver diversity combining methods play a key role in combating the detrimental effects of fading in wireless communication and other applications. A novel diversity combining method is proposed, where a universal, i.e., channel independent, orthogonal dimension-reducing space-time transformation is applied prior to quantization of the signals. The scheme may be considered as the counterpart of Alamouti modulation, and more generally of orthogonal space-time block codes.

Receiver diversity combining methods play a key role in combating the detrimental effects of fading in wireless communication and other applications. Commonly used linear diversity combining methods include maximal-ratio combining, equal-gain combining and antenna selection. A novel linear combining method is proposed where a universal, i.e., channel independent, orthogonal dimension-reducing space-time transformation is applied prior to quantization of the signals. The scheme may be considered as the counterpart of Alamouti modulation, and more generally of orthogonal space-time block codes.

Communication over the i.i.d. Rayleigh slow-fading MAC is considered, where all terminals are equipped with a single antenna. Further, a communication protocol is considered where all users transmit at (just below) the symmetric capacity (per user) of the channel, a rate which is fed back (dictated) to the users by the base station. Tight bounds are established on the distribution of the rate attained by the protocol. In particular, these bounds characterize the probability that the dominant face of the MAC capacity region contains a symmetric rate point, i.e., that the considered protocol strictly attains the sum capacity of the channel. The analysis provides a non-asymptotic counterpart to the diversity-multiplexing tradeoff of the multiple access channel. Finally, a practical scheme based on integer-forcing and space-time precoding is shown to be an effective coding architecture for this communication scenario.

Integer forcing is an equalization scheme for the multiple-input multiple-output communication channel that has been demonstrated to allow operating close to capacity for “most” channels. In this paper, the measure of “bad” channels is quantified by considering a compound channel setting, where the transmitter communicates over a fixed channel but knows only its mutual information. The transmitter encodes the data into independent streams, all taken from the same linear code. The coded streams are transmitted after applying a unitary transformation. At the receiver side, integer-forcing equalization is applied, followed by standard single-stream decoding. Considering pre-processing matrices drawn from a random ensemble, outage corresponds to the event that the target rate exceeds the achievable rate of integer forcing for a given channel matrix. For the case of the circular unitary ensemble, an explicit universal bound on the outage probability for a given target rate is derived that holds for any channel in the compound class. The derived bound depends only on the gap-to-capacity and the number of transmit antennas. The results are also applied to obtain universal bounds on the gap-to-capacity of multiple-antenna closed-loop multicast, achievable via linear pre-processed integer forcing.

The performance of integer-forcing equalization for communication over the compound multiple-input multiple-output channel is investigated. An upper bound on the resulting outage probability as a function of the gap to capacity has been derived previously, assuming a random precoding matrix drawn from the circular unitary ensemble is applied prior to transmission. In the present work a simple and explicit lower bound on the worst-case outage probability is derived for the case of a system with two transmit antennas and two or more receive antennas, leveraging the properties of the Jacobi ensemble. The derived lower bound is also extended to random space-time precoding, and may serve as a useful benchmark for assessing the relative merits of various algebraic space-time precoding schemes.

Integer-forcing source coding has been proposed as a low complexity method for compression of distributed correlated Gaussian sources. In this scheme, each encoder quantizes its observation using the same fine lattice and reduces the result modulo the coarse lattice. Rather than directly recovering the individual quantized signals, the decoder first recovers a full-rank set of judiciously chosen integer linear combinations of the quantized signals, and then inverts it. It has been observed that the method works very well for “most” but not all source covariance matrices. The present work quantifies the measure of bad covariance matrices by studying the probability that integer forcing source coding fails as a function of the rate allocated in excess of the Berger-Tung benchmark, where the probability is with respect to a random orthogonal transformation that is applied to the sources prior to quantization. For the important case where the signals to be compressed correspond to the antenna inputs of relays in an i.i.d. Rayleigh fading environment, this orthogonal transformation can be viewed as if it is performed by nature. Hence, the results provide performance guarantees for distributed source coding via integer forcing in this scenario.

Integer forcing is an equalization scheme for the multiple-input multiple-output communication channel that is applicable when all data streams are encoded using a common linear code. The scheme has been demonstrated to allow operating close to capacity for “most” channel matrices. In this work, the measure of “bad” channels is quantified by considering the outage probability of integer forcing, where random unitary precoding is applied at the transmitter side, and where the transmitter only knows the mutual information of the channel.

The integer-forcing receiver architecture has recently been proposed as a high-performance, yet low-complexity, equalization scheme, that is applicable when all data streams are encoded with the same linear code. It was further shown in [1], that this receiver architecture, when coupled with space-time linear precoding is able to achieve the capacity of the open-loop multiple-input multiple-output channel, up to a constant gap that depends only on the number of transmit antennas. The gap, however, is quite large and thus provides performance guarantees that are useful only for high values of capacity. In this work, we consider the problem of multicast over multiple-input multiple-output channels to a modest number of users, and with space-only linear precoding. It is assumed that channel state information is available to the transmitter, allowing it to optimize the precoding matrix so as to maximize the achievable transmission rate. It is numerically demonstrated that this architecture allows to very closely approach the multicast capacity at all transmission rates regimes.