Low-Density Lattice Coded Relaying With Joint Iterative Decoding

Low-density lattice codes (LDLCs) are known for their high decoding efficiency and near-capacity performance on point-to-point Gaussian channels. In this paper, we present a distributed LDLC-based cooperative relaying scheme for the multiple-access relay channel (MARC). The relay node decodes LDLC coded packets from two sources and forwards a network-coded combination to the destination. At the destination, a joint iterative decoding structure is designed to exploit the diversity gain as well as coding gain. For the LDLC-based network coding operation at the relay, we consider two alternative methods which offer a tradeoff between implementation complexity and performance, called superposition LDLC (S-LDLC) and modulo-addition LDLC (MA-LDLC). Simulation results show that the proposed scheme can provide more diversity gain and up to 6.2 dB coding gain when compared with non-cooperative LDLC coding and uncoded network-coded transmission.

In this study, the authors introduce an efficient secure channel coding (joint cryptography-channel coding) scheme based on Latin square low-density lattice codes (Latin square LDLCs) over unconstrained power additive white Gaussian noise channel. They benefit the properties of Latin square LDLCs to dramatically reduce the key size of the proposed scheme while having an acceptable level of security compared with previous similar schemes. To reduce the key size, they consider two approaches: (i) saving the generating sequence of parity-check matrix of used Latin square LDLC as the part of secret key set; (ii) employing the Hermite normal form of the generator matrix of used Latin square LDLC as the encryption matrix. To provide an acceptable level of security, they consider three other strategies: (i) applying two hard problems related to lattices, i.e. shortest basis problem and closest vector problem; (ii) using a random rational vector as the perturbation (error) vector; (iii) exploiting the special joint encryption/LDLC encoding and joint decryption/LDLC decoding algorithms. Besides, the study discusses other efficiency analysis results consisting error performance and computational complexity of the proposed scheme.

This paper presents the outage probability analysis of Joint Channel and Network Coding (JCNC) scheme in Multiple Access Relay Channel (MARC). In particular, the effect of using different interleaver patterns at different users is analysed. The motivation of this work is to show that despite its capability of achieving up to 2 dB gain in Packet Error Rate (PER), the corresponding outage probability improvement is only minimal (upper bounded at approximately 0.6 dB). This signifies that the improvement achieved by using different interleaver patterns is largely attributed by the ability of iteratively decodable codes to perform closer to the capacity limit compared to the conventional convolutional code with Soft Input Soft Output (SISO) decoder.

In this paper, we investigate the benefit of Joint Network Channel Coding (JNCC) for a new class of Multiple Access Relay Channel (MARC), defined as follows: (1) Independent sources communicate with a single destination in the presence of a relay; (2) The relay is half-duplex and applies a Selective Decode and Forward (SDF) strategy, i.e, it forwards only a deterministic function of the error-free decoded messages; (3) The sources are allowed to transmit simultaneously during the listening phase of the relay, but are constrained to remain silent during its transmission phase. We refer this model to as Semi-Orthogonal MARC (SOMARC), which leverages better the broadcast nature of the radio channel than its more conservative orthogonal counterpart, referred to as Orthogonal MARC (OMARC). All links are subject to slow fading and additive white Gaussian noise. This paper aims at measuring the advantage brought by the SOMARC over OMARC from both an information-theoretic and a practical code design perspective.

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.

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.

As a class of pseudorandom error correcting codes, generalized low-density (GLD) codes exhibit excellent performance over both additive white Gaussian noise (AWGN) and Rayleigh fading channels. In this paper, distributed GLD codes are proposed for multiple relay cooperative communications. Specifically, using the partial error detecting and error correcting capabilities of the GLD code, each relay node decodes and forwards some of the constituent codes of the GLD code to cooperatively form a distributed GLD code, which can work effectively and keep a fixed overall code rate when the number of relay nodes varies. Also, at relay nodes, a progressive processing procedure is proposed to reduce the complexity and adapt to the source-relay channel variations. At the destination, the soft information from different paths is combined for the GLD decoder thus diversity gain and coding gain are achieved simultaneously. Simulation results verify that distributed GLD codes with various number of relay nodes can obtain significant performance gains in quasistatic fading channels compared with the strategy without relays and the performance is further improved when more relays are employed.

This paper proposes a novel joint non-binary network-channel code for the Time-Division Decode-and-Forward Multiple Access Relay Channel (TD-DF-MARC), where the relay linearly combines -- over a non-binary finite field -- the coded sequences from the source nodes. A method based on an EXIT chart analysis is derived for selecting the best coefficients of the linear combination. Moreover, it is shown that for different setups of the system, different coefficients should be chosen in order to improve the performance. This conclusion contrasts with previous works where a random selection was considered. Monte Carlo simulations show that the proposed scheme outperforms, in terms of its gap to the outage probabilities, the previously published joint network-channel coding approaches. Besides, this gain is achieved by using very short-length codewords, which makes the scheme particularly attractive for low-latency applications.

Several researches investigate the performance of the conventional adaptive equalizers for the medium data rates HF waveforms (up to 8 PSK) and show that they are suitable for mitigating the HF channel. However, the performance of these types of equalizers is very bad for the high data rates HF waveforms (up to 64QAM). Most of the later researches in the high data rates HF waveforms are based on the soft turbo equalizers which are very complicated. In this paper, we try to design the lowest complex equalizer can mitigate the HF channel for the high data rates waveforms. We investigate the performance of the minimum mean square error decision feedback equalizer (MMSE-DFE) indirectly adaptive through channel estimation based on least square estimation (LS). We show that the basic performance of the MMSE-DFE cannot satisfy the standard requirements, and then we introduce two additional enhancements. First, an effective channel estimation technique (double estimation) is proposed. The new estimator shows a clear performance enhancement over simple least square estimation with linear interpolation (about 3 dB gain at 1e-5 BER for the 64QAM). The second enhancement is to use the iterative structure through decoder using the same conventional equalizer and decoder and this gives another 3 dB gain at 1e-5 BER for the 64QAM. Iterative structure is less complicated than turbo equalizers for sure, as turbo equalizers require a lot of changes in the equalizer, decoder and demapper blocks to be SISO modules. Final equalizer model satisfies all the strict requirements of both (STANAG 4539 annex B) and (MIL-STD-188-110B app. C) standards under the ITU-R Poor channel conditions. In addition, we compare our performance with two different vendors of HF modems and other different research and show that our performance is very competitive.

SummaryThis paper proposes an efficient uplink low‐density parity‐check (LDPC)‐coded multirelay cooperation architecture based on virtual Vertical‐Bell Labs Layered Space–Time (V‐BLAST) processing over a Rayleigh fading channel, where minimum mean square error in combination with a successive interference canceller and belief propagation‐based joint iterative decoder based on the introduced multilayer Tanner graph are effectively designed to detect and decode the corrupted received sequence at the destination. By introducing V‐BLAST transmission to coded multirelay cooperation, relays send their symbol streams simultaneously, which significantly reduce the transmission delay and provide higher transmission efficiency. The theoretical analysis and numerical results show that the proposed LDPC‐coded cooperation scheme outperforms the coded noncooperation under the same code rate and achieves a better compromise, with respect to the performance, signal delay, and encoding complexity associated to the number of relays, than the conventional LDPC‐coded cooperations without V‐BLAST transmission. This performance gain can be credited to the proposed V‐BLAST processing architecture and belief propagation‐based joint iterative decoding by the introduced multilayer Tanner graph at a receiver side. Copyright © 2013 John Wiley & Sons, Ltd.

Multiple-input multiple-output (MIMO) systems can provide two kinds of gain: diversity gain and multiplexing gain. Most existing MIMO schemes, including space-time coding and layered space-time, aim at maximizing either of them. Therefore, it is desirable to design a scheme to get a better tradeoff between the multiplexing gain and diversity gain. In this paper, a novel quasi-orthogonal group space-time (QOGST) architecture is proposed. In QOGST, the transmit stream is divided into several groups and all the groups are encoded via an inter-group space-time block encoder. Group interference suppression is adopted at the receiver. Performance is evaluated in terms of symmetric energy and it is shown that compared to the group layered space-time (GLST) architecture, the proposed QOGST can achieve a higher symmetric energy and a better diversity-multiplexing tradeoff. Simulation results validate our analysis and show that QOGST can achieve at least 3 dB gain over GLST at a FER of 10/sup -3/, for instance.

We show that a joint iterative detection and decoding algorithm compensates phase noise and laser frequency fluctuations in a 100 Gb/s coherent optical receiver with non-differential 16-QAM modulation, achieving 1 dB gain over existing solutions.

It has been shown that the SK scheme, which was proposed by Schalkwijk and Kailath, is a self-secure capacity-achieving (SSCA) feedback scheme for the Gaussian wiretap channel, i.e., the SK scheme not only achieves the feedback capacity of the Gaussian channel, but also is secure by itself and achieves the feedback secrecy capacity of the Gaussian wiretap channel. For the multi-user wiretap channels, very recently, it has been shown that Ozarow’s capacity-achieving feedback scheme for the two-user Gaussian multiple-access channel (GMAC) is the SSCA feedback scheme for the two-user Gaussian multiple-access wiretap channel (GMAC-WT). In this paper, first, we propose a SSCA feedback scheme for the two-user GMAC-WT with degraded message sets (GMAC-WT-DMS). Next, we extend the above scheme to the two-user GMAC-WT-DMS with noncausal channel state information at the transmitters (NCSIT), and show that the extended scheme is also a SSCA feedback scheme. Finally, we derive outer bounds on the secrecy capacity regions of the two-user GMAC-WT-DMS with or without NCSIT, and numerical results show the rate gains by the feedback.

Massive Machine Type Communication (mMTC) enables novel applications but its dense deployment and short packet properties lead to new challenges for physical layer design. This paper investigates hyper-dimensional modulation (HDM), a recently proposed novel non-orthogonal modulation, for short packet communications with superior interference tolerance in mMTC. We propose a new tree-based K-best decoding algorithm for HDM to improve the packet error rate performance in both additive white Gaussian noise (AWGN) and interference-limited scenarios. Simulation results show that the proposed algorithm can achieve 0.5 - 4 dB gain in AWGN and interference-limited channels compared to the Polar code with CRC (cyclic redundancy check)-aided list decoding.

In recent years, space-time (ST) code has been widely applied in wireless communications. However, due to interference or signal attenuation, the performance may be degraded when the data stream is transmitted through a wireless mobile fading channel. The ST block code is an effective approach, which can provide robustness by increasing the diversity gain. In this paper, five ST-OFDM systems with different code rates are presented. Moreover, a Walsh-Hadamard (WH) transform is employed as a pre-coder to form a new WH-ST-OFDM scheme. It provides a low peak-to-average power ratio at the transmitter and a significant diversity gain at the receiver. Simulation results show that the bit error rate (BER) performance of the 4x1 ST-OFDM system with code rate 1/2 is the best among all five systems due to the highest diversity gain; and the BER of the WH-ST-OFDM system is better than that of the ST-OFDM system.