Building on the work of Horstein, Shayevitz and Feder, and Naghshvar \emph{et al.}, this paper presents algorithms for low-complexity sequential transmission of a $k$-bit message over the binary symmetric channel (BSC) with full, noiseless feedback. To lower complexity, this paper shows that the initial $k$ binary transmissions can be sent before any feedback is required and groups messages with equal posteriors to reduce the number of posterior updates from exponential in $k$ to linear in $k$. Simulation results demonstrate that achievable rates for this full, noiseless feedback system approach capacity rapidly as a function of average blocklength, faster than known finite-blocklength lower bounds on achievable rate with noiseless active feedback and significantly faster than finite-blocklength lower bounds for a stop feedback system.
We consider coding schemes for channels with non-uniform inputs (NUI), where standard linear block codes can not be applied directly. We show that multilevel coding (MLC) with a set of linear codes and a deterministic mapper can achieve the information rate of the channel with NUI. The mapper, however, does not have to be one-to-one. As an application of the proposed MLC scheme, we present a rateless transmission scheme over the binary symmetric channel (BSC).
We consider the transmission of nonexponentially many messages through a binary symmetric channel with noiseless feedback. We obtain an upper bound for the best decoding error exponent. Combined with the corresponding known lower bound, this allows to find the reliability function for this channel at zero rate.
We provide a practical implementation of the rubber method of Ahlswede et al. for binary alphabets. The idea is to create the "skeleton" sequence therein via an arithmetic decoder designed for a particular $k$-th order Markov chain. For the stochastic binary symmetric channel, we show that the scheme is nearly optimal in a strong sense for certain parameters.
For information transmission a binary symmetric channel is used. There is also another noisy binary symmetric channel (feedback channel), and the transmitter observes without delay all the outputs of the forward channel via that feedback channel. The transmission of an exponential number of messages (i.e. the transmission rate is positive) is considered. The achievable decoding error exponent for such a combination of channels is investigated. It is shown that if the crossover probability of the feedback channel is less than a certain positive value, then the achievable error exponent is bette…
In this paper, we consider the problem of sequential transmission over the binary symmetric channel (BSC) with full, noiseless feedback. Naghshvar et al. proposed a one-phase encoding scheme, for which we refer to as the small-enough difference (SED) encoder, which can achieve capacity and Burnashev's optimal error exponent for symmetric binary-input channels. They also provided a non-asymptotic upper bound on the average blocklength, which implies an achievability bound on rates. However, their achievability bound is loose compared to the simulated performance of SED encoder, and even lies be…
For the information transmission a binary symmetric channel is used. There is also another noisy binary symmetric channel (feedback channel), and the transmitter observes without delay all the outputs of the forward channel via that feedback channel. The transmission of a nonexponential number of messages (i.e. the transmission rate equals zero) is considered. The achievable decoding error exponent for such a combination of channels is investigated. It is shown that if the crossover probability of the feedback channel is less than a certain positive value, then the achievable error exponent is…
In this paper, we consider the problem of variable-length coding over the class of memoryless binary asymmetric channels (BACs) with noiseless feedback, including the binary symmetric channel (BSC) as a special case. In 2012, Naghshvar et al. introduced an encoding scheme, which we refer to as the small-enough-difference (SED) encoder, which asymptotically achieves both capacity and Burnashev's optimal error exponent for symmetric binary-input channels. Building on the work of Naghshvar et al., this paper extends the SED encoding scheme to the class of BACs and develops a non-asymptotic upper …
For information transmission a discrete time channel with independent additive Gaussian noise is used. There is also feedback channel with independent additive Gaussian noise, and the transmitter observes without delay all outputs of the forward channel via that feedback channel. Transmission of nonexponential number of messages is considered and the achievable decoding error exponent for such a combination of channels is investigated. It is shown that for any finite noise in the feedback channel the achievable error exponent is better than similar error exponent of the no-feedback channel. Me…
In this paper we introduce a fundamental principle for optimal communication over general memoryless channels in the presence of noiseless feedback, termed posterior matching. Using this principle, we devise a (simple, sequential) generic feedback transmission scheme suitable for a large class of memoryless channels and input distributions, achieving any rate below the corresponding mutual information. This provides a unified framework for optimal feedback communication in which the Horstein scheme (BSC) and the Schalkwijk-Kailath scheme (AWGN channel) are special cases. Thus, as a corollary, …
Horstein, Burnashev, Shayevitz and Feder, Naghshvar et al. and others have studied sequential transmission of a K-bit message over the binary symmetric channel (BSC) with full, noiseless feedback using posterior matching. Yang et al. provide an improved lower bound on the achievable rate using martingale analysis that relies on the small-enough difference (SED) partitioning introduced by Naghshvar et al. SED requires a relatively complex encoder and decoder. To reduce complexity, this paper replaces SED with relaxed constraints that admit the small enough absolute difference (SEAD) partitionin…
Consider a binary linear code of length $N$, minimum distance $d_{\text{min}}$, transmission over the binary erasure channel with parameter $0 < ε< 1$ or the binary symmetric channel with parameter $0 < ε< \frac12$, and block-MAP decoding. It was shown by Tillich and Zemor that in this case the error probability of the block-MAP decoder transitions "quickly" from $δ$ to $1-δ$ for any $δ>0$ if the minimum distance is large. In particular the width of the transition is of order $O(1/\sqrt{d_{\text{min}}})$. We strengthen this result by showing that under suitable conditions on the weight distrib…
For information transmission a discrete time channel with independent additive Gaussian noise is used. There is also another channel with independent additive Gaussian noise (the feedback channel), and the transmitter observes without delay all outputs of the forward channel via that channel. Transmission of nonexponential number of messages is considered (i.e. transmission rate equals zero) and the achievable decoding error exponent for such a combination of channels is investigated. The transmission method strengthens the method used by authors earlier for BSC and Gaussian channels. In parti…
This paper presents a reliability-based decoding scheme for variable-length coding with feedback and demonstrates via simulation that it can achieve higher rates than Polyanskiy et al.'s random coding lower bound for variable-length feedback (VLF) coding on both the BSC and AWGN channel. The proposed scheme uses the reliability output Viterbi algorithm (ROVA) to compute the word error probability after each decoding attempt, which is compared against a target error threshold and used as a stopping criterion to terminate transmission. The only feedback required is a single bit for each decoding…
This paper presents a variable-length decision-feedback scheme that uses tail-biting convolutional codes and the tail-biting Reliability-Output Viterbi Algoritm (ROVA). Comparing with recent results in finite-blocklength information theory, simulation results for both the BSC and the AWGN channel show that the decision-feedback scheme using ROVA can surpass the random-coding lower bound on throughput for feedback codes at average blocklengths less than 100 symbols. This paper explores ROVA-based decision feedback both with decoding after every symbol and with decoding limited to a small number…
In this paper, a general binary-input binary-output (BIBO) channel is investigated in the presence of feedback and input constraints. The feedback capacity and the optimal input distribution of this setting are calculated for the case of an $(1,\infty)$-RLL input constraint, that is, the input sequence contains no consecutive ones. These results are obtained via explicit solution of a corresponding dynamic programming optimization problem. A simple coding scheme is designed based on the principle of posterior matching, which was introduced by Shayevitz and Feder for memoryless channels. The po…
The growing need for reliable communication over untrusted networks has caused a renewed interest in adversarial channel models, which often behave much differently than traditional stochastic channel models. Of particular practical use is the assumption of a \textit{causal} or \textit{online} adversary who is limited to causal knowledge of the transmitted codeword. In this work, we consider stochastic-adversarial mixed noise models. In the set-up considered, a transmit node (Alice) attempts to communicate with a receive node (Bob) over a binary erasure channel (BEC) or binary symmetric channe…
We consider a unit memory channel, called Binary State Symmetric Channel (BSSC), in which the channel state is the modulo2 addition of the current channel input and the previous channel output. We derive closed form expressions for the capacity and corresponding channel input distribution, of this BSSC with and without feedback and transmission cost. We also show that the capacity of the BSSC is not increased by feedback, and it is achieved by a first order symmetric Markov process.
In this paper we propose a feedback scheme for transmitting secret messages between two legitimate parties, over an eavesdropped communication link. Relative to Wyner's traditional encoding scheme \cite{wyner1}, our feedback-based encoding often yields larger rate-equivocation regions and achievable secrecy rates. More importantly, by exploiting the channel randomness inherent in the feedback channels, our scheme achieves a strictly positive secrecy rate even when the eavesdropper's channel is less noisy than the legitimate receiver's channel. All channels are modeled as binary and symmetric (…
In this report, the fundamental limits of simultaneous information and energy transmission in the two-user Gaussian multiple access channel (G-MAC) with and without feedback are fully characterized. More specifically, all the achievable information and energy transmission rates (in bits per channel use and energy-units per channel use, respectively) are identified. Furthermore, the fundamental limits on the individual and sum- rates given a minimum energy rate ensured at an energy harvester are also characterized. In the case without feedback, an achievability scheme based on power-splitting a…
In this paper, we consider an unmanned aerial vehicle (UAV) based wireless network using non-orthogonal multiple access (NOMA) transmission in millimeter-wave frequencies to deliver broadband data in a spectrally efficient fashion at hotspot scenarios. The necessity for the NOMA transmitter to gather information on user channel quality becomes a major drawback in practical deployments. We therefore consider various limited feedback schemes for NOMA transmission, to relieve the complexity of tracking and feeding back the full channel state information (CSI) of the users. In particular, through …
Introducing non-orthogonal multiple access (NOMA) transmission to an unmanned aerial vehicle (UAV) based communication network is a promising solution to enhance its spectral efficiency. However, for realistic deployment of such a network, identifying a practical user feedback scheme for NOMA is essential. In this paper, considering two practical feedback schemes we introduce NOMA transmission to UAVs acting as aerial base stations (BS) to provide coverage at a large stadium. In particular, a UAV-BS generates directional beams, and multiple users are served simultaneously within the same beam …
We consider multi--hop networks comprising Binary Symmetric Channels ($\mathsf{BSC}$s). The network carries unicast flows for multiple users. The utility of the network is the sum of the utilities of the flows, where the utility of each flow is a concave function of its throughput. Given that the network capacity is shared by the flows, there is a contention for network resources like coding rate (at the physical layer), scheduling time (at the MAC layer), etc., among the flows. We propose a proportional fair transmission scheme that maximises the sum utility of flow throughputs subject to the…
In this paper, the one-sided secrecy of two-way wiretap channel with feedback is investigated, where the confidential messages of one user through multiple transmissions is guaranteed secure against an external eavesdropper. For one thing, one-sided secrecy satisfies the secure demand of many practical scenarios. For another, the secrecy is measured over many blocks since the correlation between eavesdropper's observation and the confidential messages in successive blocks, instead of secrecy measurement of one block in previous works. Thus, firstly, an achievable secrecy rate region is derived…
We present an upper bound on the error probability achievable using variable-length stop feedback codes, for a fixed size of the information payload and a given constraint on the maximum latency and the average service time. Differently from the bound proposed in Polyanskiy et al. (2011), which pertains to the scenario in which the stop signal is sent over a noiseless feedback channel, our bound applies to the practically relevant setup in which the feedback link is noisy. By numerically evaluating our bound, we illustrate that, for fixed latency and reliability constraints, noise in the feedb…
A transmitter Alice may wish to reliably transmit a message to a receiver Bob over a binary symmetric channel (BSC), while simultaneously ensuring that her transmission is deniable from an eavesdropper Willie. That is, if Willie listening to Alice's transmissions over a "significantly noisier" BSC than the one to Bob, he should be unable to estimate even whether Alice is transmitting. We consider two scenarios. In our first scenario, we assume that the channel transition probability from Alice to Bob and Willie is perfectly known to all parties. Here, even when Alice's (potential) communicatio…
The Accumulative Iterative Code (AIC) proposed in this work is a new error correcting code for channels with feedback. AIC sends the information message to the receiver in a number of transmissions, where the initial transmission contains the uncoded message and each subsequent transmission informs the receiver about the locations of the errors that corrupted the previous transmission. Error locations are determined based on the forward channel output, which is made available to the transmitter through the feedback channel. AIC achieves arbitrarily low error rates, thereby being suitablefor ap…
We present an optimized secure multi-antenna transmission approach based on artificial-noise-aided beamforming, with limited feedback from a desired single-antenna receiver. To deal with beamformer quantization errors as well as unknown eavesdropper channel characteristics, our approach is aimed at maximizing throughput under dual performance constraints - a connection outage constraint on the desired communication channel and a secrecy outage constraint to guard against eavesdropping. We propose an adaptive transmission strategy that judiciously selects the wiretap coding parameters, as well …
In this paper, we address the problem of interference alignment (IA) over MIMO interference channels with limited channel state information (CSI) feedback based on quantization codebooks. Due to limited feedback and hence imperfect IA, there are residual interferences across different links and different data streams. As a result, the performance of IA is greatly related to the CSI accuracy (namely number of feedback bits) and the number of data streams (namely transmission mode). In order to improve the performance of IA, it makes sense to optimize the system parameters according to the chann…
We show that $T$ rounds of interaction over the binary symmetric channel $BSC_{1/2-ε}$ with feedback can be simulated with $O(ε^2 T)$ rounds of interaction over a noiseless channel. We also introduce a more general "energy cost" model of interaction over a noisy channel. We show energy cost to be equivalent to external information complexity, which implies that our simulation results are unlikely to carry over to energy complexity. Our main technical innovation is a self-reduction from simulating a noisy channel to simulating a slightly-less-noisy channel, which may have other applications in …
Base station (BS) cooperative transmission, also known as coordinated multi-point transmission (CoMP), is an effective way to avoid inter-cell interference in universal frequency reuse cellular systems. To gain the promised benefit, however, huge feedback overhead is in demand to gather the channel information. In this paper, we analyze the impact of channel asymmetry, which is inherent in CoMP systems, on downlink BS cooperative transmission with limited feedback. We analyze the per-user rate loss of a multi-user CoMP system led by quantization. Per-cell quantization of multicell channels is …
In this paper a MIMO quasi static block fading channel with finite N-ary delay-free, noise-free feedback is considered. The transmitter uses a set of N Space-Time Block Codes (STBCs), one corresponding to each of the N possible feedback values, to encode and transmit information. The feedback function used at the receiver and the N component STBCs used at the transmitter together constitute a Finite Feedback Scheme (FFS). Although a number of FFSs are available in the literature that provably achieve full-diversity, there is no known universal criterion to determine whether a given arbitrary F…
This paper studies the wireless spectrum sharing between a pair of distributed primary radio (PR) and cognitive radio (CR) links. Assuming that the PR link adapts its transmit power and/or rate upon receiving an interference signal from the CR and such transmit adaptations are observable by the CR, this results in a new form of feedback from the PR to CR, refereed to as hidden PR feedback, whereby the CR learns the PR's strategy for transmit adaptations without the need of a dedicated feedback channel from the PR. In this paper, we exploit the hidden PR feedback to design new learning and tran…
The paper is devoted to the analysis of problems appearing in optimisation and improvement of the power-bandwidth efficiency of digital communication feedback systems (FCS). There is shown that unlike digital systems, adaptive FCS with the analogue forward transmission allow full optimisation and derivation of optimal transmission-reception algorithm approaching their efficiency to the Shannon boundary. Differences between the forward channel capacity and capacity of adaptive FCS as communication unit, as well as their influence of the power-bandwidth efficiency of transmission are considered.
In this paper, we study the optimal training and data transmission strategies for block fading multiple-input multiple-output (MIMO) systems with feedback. We consider both the channel gain feedback (CGF) system and the channel covariance feedback (CCF) system. Using an accurate capacity lower bound as a figure of merit, we investigate the optimization problems on the temporal power allocation to training and data transmission as well as the training length. For CGF systems without feedback delay, we prove that the optimal solutions coincide with those for non-feedback systems. Moreover, we sh…
We study the asymptotic outage performance of incremental redundancy automatic repeat request (INR-ARQ) transmission over the multiple-input multiple-output (MIMO) block-fading channels with discrete input constellations. We first show that transmission with random codes using a discrete signal constellation across all transmit antennas achieves the optimal outage diversity given by the Singleton bound. We then analyze the optimal SNR-exponent and outage diversity of INR-ARQ transmission over the MIMO block-fading channel. We show that a significant gain in outage diversity is obtained by prov…
Performing link adaptation in a multiantenna and multiuser system is challenging because of the coupling between precoding, user selection, spatial mode selection and use of limited feedback about the channel. The problem is exacerbated by the difficulty of selecting the proper modulation and coding scheme when using orthogonal frequency division multiplexing (OFDM). This paper presents a data-driven approach to link adaptation for multiuser multiple input mulitple output (MIMO) OFDM systems. A machine learning classifier is used to select the modulation and coding scheme, taking as input the …
The transmission of a Gaussian source over a block-fading multiple antenna channel in the presence of a feedback link is considered. The feedback link is assumed to be an error and delay free link of capacity 1 bit per channel use. Under the short-term power constraint, the optimal exponential behavior of the end-to-end average distortion is characterized for all source-channel bandwidth ratios. It is shown that the optimal transmission strategy is successive refinement source coding followed by progressive transmission over the channel, in which the channel block is allocated dynamically amon…
This work focuses on the minimum transmission energy required for communicating a pair of correlated Gaussian sources over a two-user Gaussian broadcast channel with noiseless and causal channel output feedback (GBCF). We study the fundamental limit on the required transmission energy for broadcasting a pair of source samples, such that each source can be reconstructed at its respective receiver to within a target distortion, when the source-channel bandwidth ratio is not restricted. We derive a lower bound and three distinct upper bounds on the minimum required energy. For the upper bounds we…
This paper presents a general approach for optimizing the number of symbols in increments (packets of incremental redundancy) in a feedback communication system with a limited number of increments. This approach is based on a tight normal approximation on the rate for successful decoding. Applying this approach to a variety of feedback systems using non-binary (NB) low-density parity-check (LDPC) codes shows that greater than 90% of capacity can be achieved with average blocklengths fewer than 500 transmitted bits. One result is that the performance with ten increments closely approaches the p…
This paper proposes an adaptive multi-mode transmission strategy to improve the spectral efficiency achieved in the multiple-input multiple-output (MIMO) broadcast channel with delayed and quantized channel state information. The adaptive strategy adjusts the number of active users, denoted as the transmission mode, to balance transmit array gain, spatial division multiplexing gain, and residual inter-user interference. Accurate closed-form approximations are derived for the achievable rates for different modes, which help identify the active mode that maximizes the average sum throughput for …
Visible light communications (VLC) is an emerging technology with a promise of viable solution to spectrum crunch problem in conventional radio frequency (RF) bands. In this work, we consider a downlink multiuser VLC network where users randomly change their location and vertical orientation. In order to increase the spectral efficiency, we consider the non-orthogonal multiple access (NOMA) transmission to serve multiple users simultaneously. In particular, we propose individual and group-based user ordering techniques for NOMA with various user feedback schemes. In order to reduce the computa…
In this paper, we investigate the necessity of finite blocklength codes in distributed transmission of independent message sets over channels with feedback. Previously, it was shown that finite effective length codes are necessary in distributed transmission and compression of sources. We provide two examples of three user interference channels with feedback where codes with asymptotically large effective lengths are sub-optimal. As a result, we conclude that coded transmission using finite effective length codes is necessary to achieve optimality. We argue that the sub-optimal performance of …
To achieve the available performance gains in half-duplex wireless relay networks, several cooperative schemes have been earlier proposed using either distributed space-time coding or distributed beamforming for the transmitter without and with channel state information (CSI), respectively. However, these schemes typically have rather high implementation and/or decoding complexities, especially when the number of relays is high. In this paper, we propose a simple low-rate feedback-based approach to achieve maximum diversity with a low decoding and implementation complexity. To further improve …
The transmission capacity of an ad-hoc network is the maximum density of active transmitters per unit area, given an outage constraint at each receiver for a fixed rate of transmission. Most prior work on finding the transmission capacity of ad-hoc networks has focused only on one-way communication where a source communicates with a destination and no data is sent from the destination to the source. In practice, however, two-way or bidirectional data transmission is required to support control functions like packet acknowledgements and channel feedback. This paper extends the concept of transm…
This paper presents a method for computing a finite-blocklength converse for the rate of fixed-length codes with feedback used on discrete memoryless channels (DMCs). The new converse is expressed in terms of a stochastic control problem whose solution can be efficiently computed using dynamic programming and Fourier methods. For channels such as the binary symmetric channel (BSC) and binary erasure channel (BEC), the accuracy of the proposed converse is similar to that of existing special-purpose converse bounds, but the new converse technique can be applied to arbitrary DMCs. We provide exam…
We consider the optimal design of sequential transmission over broadcast channel with nested feedback. Nested feedback means that the channel output of the outer channel is also available at the decoder of the inner channel. We model the communication system as a decentralized team with three decision makers---the encoder and the two decoders. Structure of encoding and decoding strategies that minimize a total distortion measure over a finite horizon are determined. The results are applicable for real-time communication as well as for the information theoretic setup.
In this paper, we consider encoding strategies for the Z-channel with noiseless feedback. We analyze the combinatorial setting where the maximum number of errors inflicted by an adversary is proportional to the number of transmissions, which goes to infinity. Without feedback, it is known that the rate of optimal asymmetric-error-correcting codes for the error fraction $τ\ge 1/4$ vanishes as the blocklength grows. In this paper, we give an efficient feedback encoding scheme with $n$ transmissions that achieves a positive rate for any fraction of errors $τ<1$ and $n\to\infty$. Additionally, we …
This paper presents a decentralized relay selection protocol for a dense wireless network and describes channel feedback strategies that improve its performance. The proposed selection protocol supports hybrid automatic-repeat-request transmission where relays forward parity information to the destination in the event of a decoding error. Channel feedback is employed for refining the relay selection process and for selecting an appropriate transmission mode in a proposed adaptive modulation transmission framework. An approximation of the throughput of the proposed adaptive modulation strategy …
This paper quantifies the fundamental limits of variable-length transmission of a general (possibly analog) source over a memoryless channel with noiseless feedback, under a distortion constraint. We consider excess distortion, average distortion and guaranteed distortion ($d$-semifaithful codes). In contrast to the asymptotic fundamental limit, a general conclusion is that allowing variable-length codes and feedback leads to a sizable improvement in the fundamental delay-distortion tradeoff. In addition, we investigate the minimum energy required to reproduce $k$ source samples with a given f…
Obtaining accurate global channel state information (CSI) at multiple transmitter devices is critical to the performance of many coordinated transmission schemes. Practical CSI local feedback often leads to noisy and partial CSI estimates at each transmitter. With rate-limited bi-directional backhaul, transmitters have the opportunity to exchange few CSI-related bits to establish global channel state information at transmitter (CSIT). This work investigates possible strategies towards this goal. We propose a novel decentralized algorithm that produces minimum mean square error (MMSE)-optimal g…
Traditional channel coding with feedback constructs and transmits a codeword only after all message bits are available at the transmitter. This paper joins Guo & Kostina and Lalitha et. al. in developing approaches for causal (or progressive) encoding, where the transmitter may begin transmitting codeword symbols as soon as the first message bit arrives. Building on the work of Horstein, Shayevitz and Feder, and Naghshvar et. al., this paper extends our previous computationally efficient systematic algorithm for traditional posterior matching to produce a four-phase encoder that progressively …
