A lattice compress-and-forward scheme

Results for Gaussian relay channels typically focus on maximizing transmission rates for given locations of the source, relay and destination. We introduce an alternative perspective, where the objective is maximizing coverage for a given rate. The new objective captures the problem of how to deploy relays to provide a given level of service to a particular geographic area, where the relay locations become a design parameter that can be optimized. We evaluate the decode and forward (DF) and compress and forward (CF) strategies for the relay channel with respect to the new objective of maximizing coverage. When the objective is maximizing rate, different locations of the destination favor different strategies. When the objective is coverage for a given rate, and the relay is able to decode, DF is uniformly superior in that it provides coverage at any point served by CF. When the channel model is modified to include random fading, we show that the monotone ordering of coverage regions is not always maintained. While the coverage provided by DF is sensitive to changes in the location of the relay and the path loss exponent, CF exhibits a more graceful degradation with respect to such changes. The techniques used to approximate coverage regions are new and may be of independent interest.

Consider a slowly fading Gaussian relay channel where the source is not aware of channel state information (CSI) and the relay is only partially aware of CSI. As a single cooperation strategy, Decode-and-Forward (DF) or Compress-and-Forward (CF), is not the best for all channel states, the relay should be able to switch between them according to its CSI. However as the source cannot be aware of chosen cooperative strategy, it should use so called oblivious codes that perform equally well under different cooperative strategies. In this paper, we prove that doubly nested lattice codes is an oblivious code which can be used to achieve DF, CF or point-to-point rate in the relay channels. Using the oblivious lattice coding, the relay, according to its CSI, decides to use DF, CF or no cooperation at all. We show that inner bound on outage probability is significantly improved if the oblivious lattice code is used with selective coding strategy at the relay.

Consider the composite relay channel consisting of a set of relay channels associated to a probability measure. The current channel is a draw from its probability and in some cases arbitrary small error probability cannot be guaranteed for all channels in the set. In this paper, instead of finding the maximum achievable rate subject to a small error probability (EP) for all the channels in the set, we look at the asymptotic behavior of EP for a given rate. The notion of achievable EP is introduced as a novel performance measure for wireless relay channels. We can intuitively define it as the smallest EP that can be asymptotically achieved for a given rate. The behavior of EP is directly related to the ϵ-capacity of each channel in the set. It is shown that the behavior of EP is upper and lower bounded by the outage probability of a region which is referred to as the full error region. Then every code with a rate belonging to this region yields EP equal to one. Finally, new coding for oblivious cooperation simultaneously exploiting both Decode-and-Forward (DF) and Compress-and-Forward (CF) strategies is investigated. The Gaussian relay channel with slow fading is also discussed.

Previously, it has been shown that more feedback links may help to achieve larger finite blocklength rates of the Gaussian relay channel (GRC). However, this is only built on the idealistic assumption that the feedback channels are noise free. In this paper, we revisit the GRC with feedback by considering the situation that the feedback channels are also corrupted by additive white Gaussian noises. For given coding blocklength and decoding error probability, achievable rates of our proposed schemes are characterized. Numerical results show that comparing with those schemes of the same model without using feedback, there may still exist rate gain even the feedback channels are corrupted by noises. Besides this, we also show that comparing with the existing feedback scheme for the GRC with one noise-free feedback link, two noisy feedback links still bring rate gain for some cases.

In a bi-directional relay channel, two nodes wish to exchange independent messages over a shared wireless half-duplex channel with the help of a relay. In this paper, we derive achievable rate regions for four new half-duplex protocols and compare these to four existing half-duplex protocols and outer bounds. In time, our protocols consist of either two or three phases. In the two phase protocols, both users simultaneously transmit during the first phase and the relay alone transmits during the second phase, while in the three phase protocol the two users sequentially transmit followed by a transmission from the relay. The relay may forward information in one of four manners; we outline existing amplify and forward (AF), decode and forward (DF), lattice based, and compress and forward (CF) relaying schemes and introduce the novel mixed forward scheme. The latter is a combination of CF in one direction and DF in the other. We derive achievable rate regions for the CF and Mixed relaying schemes for the two and three phase protocols. We provide a comprehensive treatment of eight possible half-duplex bi-directional relaying protocols in Gaussian noise, obtaining their relative performance under different SNR and relay geometries.

The Schalkwijk-Kailath (SK) scheme for the AWGN channel with noise-free feedback is well-known since its coding complexity grows linearly with the coding blocklength, and it is capacity-achieving and has extremely lower decoding error probability comparing with existing excellent codes such as LDPC and Polar codes. However, extension of SK scheme to more practical scenarios is challenging since it depends heavily on the feedback success. This paper aims to investigate how to design SK-type schemes for channels with intermittent feedback and establish the relationship between the coding blocklength, the desired decoding error probability, the achievable transmission rate and secrecy level of our proposed schemes. Specifically, first, for the additive white Gaussian noise (AWGN) channel with intermittent noise-free feedback, a variation of the well-known Schalkwijk-Kailath (SK) scheme for the AWGN channel with noise-free feedback is proposed, and the corresponding achievable rate is characterized for given coding blocklength and decoding error probability. Subsequently, the proposed scheme is extended to channels with noisy intermittent feedback. To quantitatively evaluate the secrecy performance, we adopt the eavesdropper's normalized equivocation as the secrecy metric and analytically characterize the achievable secrecy level of the proposed schemes. In particular, we show that perfect weak secrecy, i.e., asymptotically vanishing information leakage rate, can be achieved under certain conditions. Numerical results show that for a given decoding error probability threshold, our proposed schemes require lower signal-to-noise ratio and significantly shorter coding blocklength comparing with LDPC code. The study of this paper may provide a way to construct efficient coding scheme for channels in the presence of intermittent feedback.

In this letter, the Gaussian two-way relay channel with direct links is investigated in which two users aim at exchanging their messages with the help of a relay node. We propose a new lattice-based compress-and-forward strategy and obtain its achievable rate-region. We show that the proposed scheme is superior to all previously known achievable schemes for channel gains larger than one. In particular, under the symmetric case, the proposed scheme is able to achieve a capacity region within 0.5 bit or (1/2) log3 ≅ 0.79 bit, depending on the power of the relay.

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> This work considers the problem of communication between a remote single transmitter and a destined user, with helping colocated users, over an independent block Rayleigh-fading channel. The colocation nature of the users allows cooperation, which increases the overall achievable rate, from transmitter to destination. The transmitter is ignorant of the fading coefficients, while receivers have access to perfect channel state information (CSI). We propose, for this setting, a multilayer broadcast transmission approach. The broadcast approach enables enhanced cooperation between the colocated users. That is due to the nature of broadcasting, where the better the channel quality, the more layers that can reliably be decoded. The cooperation between the users is performed over additive white Gaussian noise (AWGN) channels, with a relaying power constraint, and unlimited bandwidth. Three commonly used cooperation techniques are studied: amplify-and-forward (AF), compress–and-forward (CF), and decode–and-forward (DF). These techniques are extended by using the broadcast approach for the case of relaxed decoding delay constraint. For this case, a separate processing of the layers, which includes multisession cooperation is shown to be beneficial. Further, closed-form expressions for infinitely many AF sessions and recursive expressions for the more complex CF are given. Numerical results for the various cooperation strategies demonstrate how the multisession cooperation outperforms conventional relaying techniques. </para>

The increasing demand for high-density and high-speed digital optical recording systems has made the development of advanced coding and signal processing techniques for fast and reliable data recovery increasingly important. In recent years, the parity-check (PC)-code-based reception technique has been widely studied for magnetic recording systems, and it is projected to be highly promising for high-density optical recording. The PC code is an inner error correction code (ECC), which can detect dominant short error events of the system, using only a few parity bits. This reduces the loss in error correction capability of the outer ECC due to random short errors and results in a simple and efficient solution to improve the overall performance. This thesis is dedicated to the design and analysis of PCcode- based recording systems to achieve higher recording capacity with low implementation complexity, for high-density blue laser disc systems. In particular, most of the key components of the PC-code-based optical recording system have been designed and optimized for different recording densities, and different proportions of white noise and media noise. During the development of advanced coding and detection techniques, it becomes necessary to investigate the system’s performance with different coding schemes and recording densities. In Chapter 2 of the thesis, we propose a generalized Braat-Hopkins model for optical recording channels, which provides a fair basis for the performance comparison of detection schemes over different coding schemes and recording densities, for channels with additive, white Gaussian noise (AWGN) and media noise. Various basic issues associated with the PC-code-based systems are investigated in Chapter 3. These include bounds for bit error rates and error event probabilities, the dominant error events at channel detector output, different PC codes, simple and efficient post-processors, the impact of error events that are split across data block boundaries and the corresponding remedy, as well as the effects of code rates and recording densities. Simulation results show that a 4-bit PC code achieves the best performance. The corresponding bit error rates (BERs) are very close to the performance bounds, at both nominal and high densities. Constrained codes, which serve as a key component in the read-write channel of data storage systems, are desired to have a high code rate with low-complexity encoder/decoder. In Chapter 4, we investigate the design of certain capacity-approaching constrained codes for optical recording systems. In particular, we derive analytically the relationship between the number of encoder states and the maximum size of these codes. We identify the minimum number of encoder states that maximizes the code rate, for any desired codeword length. The design of constrained PC codes is key to the development of PCcode- based systems, and the systematic design of efficient constrained PC codes remains a challenging problem. In Chapter 5, we propose a general and systematic code design technique for constructing capacity-approaching constrained PC codes, which can detect any type of error events of the system, with the minimum code rate loss. Compared to the rate 2/3 code without parity, the newly designed constrained 4-bit PC code achieves a performance gain of 2 dB at nominal density, and 1.5 dB at high density, at BER = 10-5. As the dominant noise for high-density optical recording systems, media noise severely degrades the performance of channel detectors and postprocessors that are designed for AWGN. In Chapter 6, we propose two novel modifications to the bit detector to combat media noise. We further develop a data-dependent post-processing scheme for error correction. Compared to the system designed without considering media noise and without PC codes, the overall performance gain of the developed scheme can be more than 11 dB at high media noise levels. In data storage systems, the ECC failure rate (EFR) serves as the ultimate measure of the data recovery performance. In Chapter 7, we develop semi-analytical approaches for estimating the EFR, and analyze EFRs for the developed PC-code-based systems, for the cases without and with interleaving. Our analysis shows that with the optimum interleaving degrees, compared to the rate 9/13 code without parity, the 2-bit PC code achieves a gain of around 0.5 dB, and the 4-bit PC code gains 0.6 dB, at high record ing density and EFR = 10-16. The thesis concludes in Chapter 8 with some suggestions for further work.

This paper is concerned with the Gaussian relay channel (GRC) under the one-code constraint, where the source and the relay utilize the same code to send message. An advantage of such one-code constraint is that the error propagation resulting from re-encoding can be mitigated as the relay can forward directly the decoded “codeword” to the destination. The maximal achievable rate of the considered GRC is derived using the technique of superposition block Markov encoding based on the single code. Moreover, the forward-backward (FB) decoding strategies over the sliding window are developed both at the destination and at the relay. When LDPC codes are applied to the GRC system, a practical FB message passing decoding algorithm is presented. Simulation results show that the decoding performance can be improved as the window length increases and a small length (no greater than 4) is good enough for the FB decoding, and that re-encoding at relay may degrade the decoding performance at the destination.

In this paper, the two-user interference relay channel (IRC) is studied. Transmission schemes for this network are compared. Namely, compress-and-forward (CF) and functional decode-and-forward (FDF) are presented. In CF, the relay establishes cooperation with the users by compressing its observation and forwarding it to the receivers. In FDF, the relay decodes a linear combination of the transmitted signals, and forwards this linear combination. We compare these schemes with decode-and-forward (DF) and with a upper bound on the rates in the IRC. It turns out that these schemes outperform DF, and approach the upper bound for some cases.

This paper focuses on the full-duplex Gaussian two-way diamond relay channel (TWDRC), where two users wish to exchange their messages with the help of two relays, when one relay performs a lattice-based Compress-and-Forward (CF) scheme. The other relay performs either Decode-and-Forward (DF), Amplify-and-Forward (AF) or a lattice-based CF scheme. We start by proposing a novel lattice-based CF/CF scheme, where both relays perform CF. As opposed to the single relay case, two main challenges arise: the quantization rate region is constrained by two Multiple Access Channel (MAC) rate regions, and each user has to combine two noisy observations to decode the sent message. These challenges are tackled by exploiting MAC techniques and Maximum Ratio Combining methods, which are used to combine the two noisy observations. We then characterize a general achievable rate region when one relay sends a version of both users' messages (eventually noisy), which encompasses both AF and DF, and the other relay performs CF and derive the corresponding achievable rate regions. Finally, the three proposed relaying schemes are compared via numerical evaluations. Clearly, the position of both relays has an impact on the best relaying strategy.

SummaryIn this paper, we propose a general model to study the full‐duplex non‐coherent (NC) decode‐and‐forward Gaussian relay channel (RC) with energy harvesting (EH) nodes, called NC‐EH‐ , in three cases: (i) no energy transfer (ET), (ii) one‐way ET from the source (S) to the relay (R), and (iii) two‐way ET. We consider the problem of optimal power allocation in NC‐EH‐ in order to maximize the total transmitted bits from S to the destination in a given time duration. General stochastic energy arrivals at S and R with known EH times and values are assumed. In NC‐EH‐ with no ET, the complicated min‐max optimization form along with its constraints make the problem intractable. It is shown that this problem can be transformed to a solvable convex form; however, convex optimization solution does not provide the structural properties of the optimal solution. Therefore, following an alternative perspective, we investigate conditions on harvesting process of S and R where we find optimal algorithmic solution. Further, we propose some suboptimal algorithms and provide some examples, in which the algorithms are optimal. Moreover, we find a class of problems for NC‐EH‐ with one‐way ET from S to R, where the optimal algorithmic solution is devised. For NC‐EH‐ with two‐way ET, we propose general optimal algorithmic solution. Furthermore, the performance of the proposed algorithms are evaluated numerically and compared with optimal numerical convex optimization tools. Copyright © 2014 John Wiley &amp; Sons, Ltd.

In this paper, a decoding procedure is developed for both the compress-and-forward (CF) and the short message quantize-and-forward (QF-SM) relaying schemes. This procedure is based on exploiting a common feature of the mapping used by both schemes to determine the relay output from the estimate of its input. Using this decoding procedure, it is shown that the CF scheme achieves higher rates than both the conventional CF and the QF-SM schemes. The advantage of the proposed procedure is demonstrated in a Gaussian multicast one-message two-destination relay network and a multicast two-message three-destination network.

Polynomial Wigner Ville distribution (PWVD) is considered as a tool for recognition of signals with an unknown frequency modulation law. This time-frequency distribution (TF) with multi-linear kernel is an optimal form for signals with a polynomial frequency modulation law. Instantaneous frequency (IF) is the important property of non-stationary signals, i.e. signals whose spectral contents vary with time. Then the recognition of unknown signals can be formulated as the problem of estimation of its instantaneous frequency. The studies of estimation of IF for noiseless signals can be found in literature. The noise embedded in a signal has large influence on time-frequency distribution and can change the true value of the IF. Time-frequency distribution strongly depends on the kind of noise. In this paper signals embedded in additive gaussian and impulse noise have been considered. Estimation of the instantaneous fiequency in impulsive noise background is different than in gaussian noise and requires robust forms of time-frequency distributions. In this paper the application of the robust form of the Wigner-Ville distribution (WVD_r) and the robust form of the polynomial Wigner-Ville distribution (PWVD_r) for IF estimation is presented. Maxima of these distributions are assumed as the estimates of true values of IF. The theoretical background of WVD_r and PWVD_r distributions is introduced and several numerical experiments of IF estimation are presented.