Coding for channels with intermittent feedback and its security analysis.

In wireless communication systems, the intended receiver is able to obtain the perfect channel state information (CSI) as long as the training sequence is sufficiently long, and then through a quantized feedback channel (QFC), the transmitter gets imperfect CSI caused by the quantized noise. In general, the design of efficient coding schemes for wireless channels with imperfect CSI at the transmitter (I-CSIT) is difficult and challenging, and one possible method is to construct such a scheme by using channel feedback. In the literature, it has already been shown that the classical Schalkwijk-Kailath (SK) scheme for the additive white Gaussian noise (AWGN) channel with noiseless feedback is a highly efficient coding scheme since its coding complexity is extremely low and the decoding error doubly exponentially decays as the coding blocklength tends to infinity. Existing SK-type schemes mainly focus on the case that perfect CSI is known at the transceiver, and adopt modulo lattice function to eliminate the impact of feedback channel noise (often considered as AWGN) on the performance of SK-type schemes. However, for channels with I-CSIT and QFC, this does not work since the distribution of quantized noise is unknown and I-CSIT brings additional non-convergence estimation error to the transceiver, leading to the application of SK-type schemes to practical wireless scenarios becomes challenging. In this paper, first, for the quasi-static fading channel with I-CSIT and QFC, we design a modulo lattice based SK-type scheme where the receiver adopts an auxiliary signal to decode the message, and numerical results show that the rate of our scheme almost approaches that of the same model with perfect CSI at the transceiver and noise-free feedback for some cases. Next, we further extend the above scheme to the two-path fading scenario, which is modeled as the two-ray channel with I-CSIT and QFC. Treating the signal of the second path as a relay, our extended scheme combines the amplify-and-forward relay strategy and the previously proposed scheme for the same model without ISI. However, this extended scheme cannot be applied to multi-path fading scenario, to this end, we propose a new SK-type scheme for the multi-path fading case. The intuition behind this scheme is to transform the multi-path fading channel into a fading MIMO channel by discrete fourier transform (DFT), and then apply the SK-type scheme to the MIMO channel in frequency domain and use inverse DFT to obtain the codeword in time domain. The study of this paper may provide a way to design efficient coding scheme for fading channels in the presence of imperfect CSI and quantized feedback.

We consider the challenges of finding good puncturing patterns for rate-compatible low-density parity-check code (LDPC) codes over additive white Gaussian noise (AWGN) channels. Puncturing is a scheme to obtain a series of higher rate codes from a lower rate mother code. It is widely used in channel coding but it causes performance is lost compared to non-punctured LDPC codes at the same rate. Previous work, considered the role of survived check nodes in puncturing patterns. Limitations, such as single survived check node assumption and simulation-based verification, were examined. This paper analyzes the performance according to the role of multiple survived check nodes and multiple dead check nodes. Based on these analyses, we propose new algorithm to find a good puncturing pattern for LDPC codes over AWGN channels.

The use of open-loop coding can be easily extended to a closed-loop concatenated code if the transmitter has access to feedback. This can be done by introducing a feedback transmission scheme as an inner code. In this paper, this process is investigated for the case when a linear feedback scheme is implemented as an inner code and, in particular, over an additive white Gaussian noise (AWGN) channel with noisy feedback. To begin, we look to derive an optimal linear feedback scheme by optimizing over the received signal-to-noise ratio (SNR). From this optimization, a linear feedback scheme is produced that is asymptotically optimal in the sense of blocklength-normalized SNR; it is then compared to other well-known schemes. Then, the linear feedback scheme is implemented as an inner code to a concatenated code over the AWGN channel with noisy feedback. This code shows improvements not only in error exponent bounds, but also in bit error rate (BER) and frame error rate (FER). It is also shown that if the concatenated code has total blocklength L and the inner code has blocklength, N, the inner code blocklength should scale as N = O(C/R), where C is the capacity of the channel and R is the rate of the concatenated code. Simulations with low-density parity-check (LDPC) and turbo codes are provided to display practical applications and their error rate benefits.

Low-density Parity check codes (LDPC) are gaining interest for high data rate application in both terrestrial and spatial communications which requires low bit error rate. This paper proposes an algorithm through which the best parity check matrix is obtained for irregular low density parity check codes, which reduces the Bit Error Rate ,Frame Error Rate and computational complexity. Tanner graph also called a bipartite graph format in an Low Density Parity Check (LDPC) code design contains many short cycles; it will produce a computational complexity in a code design process and it degrades the code performance. To overcome this effect, we proposed an new algorithm which obtains a best final parity check matrix. Throughout the paper we will give the detailed description of an efficient algorithm proposed. The complexity is studied graphically and analytically. Using proposed algorithm, cycles of length four observed in corresponding matrix are removed. Each matrix is evaluated over a noisy Additive White Gaussian Noise (AWGN) channel. Bit Error rate and Frame error rate is calculated. The results are compared with randomly generated best parity check matrix. Simulation results shows that proposed method successfully overcomes the computational complexity and meets the near Shannon limit.

Harvesting energy from radio frequency signals along with transmitting data through them is appealing for different wireless communication scenarios, such as radio frequency identification (RFID) systems and implantable devices. In this paper, we propose a technique to design nonlinear codes for the use in such systems taking into account both energy transmission and error rate requirements. In particular, we propose using concatenation of a nonlinear trellis code (NLTC) with an outer low-density parity-check (LDPC) code. We design the NLTC based on maximization of its free distance. We give necessary and sufficient conditions for its catastrophicity; in order to avoid catastrophic codes, we connect each designed NLTC to a corresponding linear convolutional code allowing for the use of simpler conditions for verification. Furthermore, we use EXIT charts to design the outer LDPC code while fixing the inner NLTC. Via examples, we demonstrate that our designed codes operate at ∼ 0.8 dB away from the information theoretic limits, and they outperform both regular LDPC codes and optimized irregular LDPC codes for additive white Gaussian noise (AWGN) channels. In addition, we show that the proposed scheme outperforms the reference schemes of concatenating LDPC codes with nonlinear memoryless mappers and using classical linear block codes in a time switching mode. © 2016 IEEE.

Recently, an intensive discussion on candidate channel coding schemes for the fifth-generation (5G) mobile communication systems has been carried out both in academia and industry. We added to this discussion by providing a comparison between two capacity-achieving channel codes: Low-density Parity-Check (LDPC) codes and Polar codes. The considered codes have been selected as the standard for 5G New Radio (NR) by the 3rd Generation Partnership Project (3GPP). We investigate these codes in terms of Frame Error Rate (FER) on small and moderate length message transmission in the context of Massive Machine type communication (mMTC). Multiple decoding implementation schemes are considered for both codes and compare their error correction performance over an Additive White Gaussian Noise (AWGN) channel. The simulation results reveal that polar codes under the Cyclic redundancy code (CRC) aided Successive Cancellation list (CA-SCL) decoding performs better as compared to other decoding patterns in terms of reliability. Furthermore, we analyze the impact of CRC length on the decoding performance of CA-SCL.

Turbo Codes and Tail Biting Convolutional Codes are used for channel coding in LTE, but these codes are not pertinent in 5G. For Channel coding, advanced error correction techniques are required for the 5G. Polar codes are adopted for control information and LDPC codes are required for Data information for the 5G. Various coding techniques such as LDPC codes, Quasi Cyclic (QC)-LDPC codes, Non-Binary (NB)-LDPC codes, Spatially Coupled (SC)-LDPC codes, Irregular Repeat Accumulate (IRA) codes, Polar codes, Distributed CRC Aided (DCA) codes, and Fountain codes are illustrated. For Decoding Min-Sum Algorithm and Belief Propagation are used for LDPC codes. Min-Sum, OMS, NMS, BP methods are applied in QC-LDPC codes. SC, SCL, FSCL, CASCL, BP algorithms implemented for Polar codes. Simulation of QC-LDPC codes, Polar codes, and LDPC codes are generated by using MATLAB Software. The performance of all channel coding techniques with consideration to BER and BLER is mentioned.

This dissertation presents a systematic exposition on finite-block-length coding theory and practice. We begin with the task of identifying the maximum achievable rates over noisy, finite-block-length constrained channels, referred to as (e, n)-capacity Cen, with e denoting target block-error probability and n the block length. We characterize how the optimum codes look like over finite-block-length constrained channels. Constructing good, short-block-length error-correcting codes defined on sparse graphs is the focus of the thesis. We propose a new, general method for constructing Tanner graphs having a large girth by progressively establishing edges or connections between symbol and check nodes in an edge-by-edge manner, called progressive edge-growth (PEG) construction. Lower bounds on the girth of PEG Tanner graphs and on the minimum distance of the resulting low-density parity-check (LDPC) codes are derived in terms of parameters of the graphs. The PEG construction attains essentially the same girth as Gallager's explicit construction for regular graphs, both of which meet or exceed an extension of the Erdos-Sachs bound. The PEG construction proves to be powerful for generating good, short-block-length binary LDPC codes. Furthermore, we show that the binary interpretation of GF(2b) codes on the cycle Tanner graph TG(2, dc), if b grows sufficiently large, can be used over the binary-input additive white Gaussian noise (AWGN) channel as good code for optimum and good code for iterative decoding. Codes on sparse graphs are often decoded iteratively by a sum-product algorithm (SPA) with low complexity. We investigate efficient digital implementations of the SPA for decoding binary LDPC codes from both the architectural and algorithmic point of view, and describe new reduced-complexity derivatives thereof. The unified treatment of decoding techniques for LDPC codes provides flexibility in selecting the appropriate design point in high-speed applications from a performance, latency, and computational complexity 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.

Semialgebraic low-density parity-check (SA-LDPC) codes are proposed for the multilevel coded modulation system. We optimize code parameters of LDPC codes according to the rate of each level by Gaussian approximation. Iterative multistage decoding (IMSD) scheme is adopted to get the significant improvement. System performance with Ungerboeck partitioning (UP) and mixed partitioning (MP) for 8PSK is evaluated respectively over additive white Gaussian noise (AWGN) channels. Many results are presented, they indicate that in terms of the tradeoff between hardware complexity and system performance, constructed multilevel coded modulation system based on optimized LDPC codes, capacity rule and MP is a good choice for the bandwidth efficient transmission over AWGN channels.

A definition of least cyclostationary order (LCO) is proposed based on the inner cyclic period of single carrier and orthogonal frequency division multiplexing (OFDM) signals. The LCOs of single carrier and OFDM signals are derived. Since the LCO has a relationship with the carrier frequency offset (CFO), a blind CFO estimation scheme for single carrier and OFDM signals can be proposed. The novel scheme is entirely blind without any priori information and is proved to be the same as cumulants estimation when the LCO is known. However, the new scheme is superior to the estimation based on cumulant when the LCO is unknown. The mean-square error of M-phase shift keying signals approaches the Cramer–Rao bound in additive white Gaussian noise (AWGN) channel. Simulation results are given to verify the effectiveness of the proposed blind estimation scheme in Rician fading channel and in AWGN channel.

In this paper, we introduce Hyper-Dimensional Modulation (HDM) for massive machine-type communications (mMTC). HDM enables robust communication of short packets by spreading information bits across many elements in a hyper-dimensional vector and superimposing a set of such non-orthogonal vectors. The proposed CRC-aided K-best decoding algorithm for HDM can achieve a very low packet error rate (PER) in additive white Gaussian noise (AWGN) channels for short packets. Furthermore, extended decoding algorithms are proposed to combat overwhelming interference in an mMTC network. Comprehensive simulation and real-world experiment results show that HDM outperforms sparse superposition codes in AWGN channels and state-of-the-art short codes such as polar and tail-biting convolutional codes in interference-heavy channels for short packet transmissions.

Ultra-reliable low-latency communication (URLLC) is a key technology in future wireless communications, and finite blocklength (FBL) coding is the core of the URLLC. In this paper, FBL coding schemes for the wireless multi-antenna channels are proposed, which are based on the classical Schalkwijk-Kailath scheme for the point-to-point additive white Gaussian noise channel with noiseless feedback. Simulation examples show that the proposed feedback-based schemes almost approach the corresponding channel capacities.

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.

Polar codes [1] are a class of provably capacity-achieving error correcting codes (ECC) for memoryless symmetric channels with low-complexity code structures; they have been shown to enjoy better decoding performance over LDPC and Turbo codes under certain scenarios. In this work, we study the application of polar codes for NAND-based SSDs, and mainly focus on the joint source channel coding (JSCC) aspect of polar codes for flash data protection. In a practical SSD system, in addition to the host data, both flash translation layer (FTL) and host side will write on NAND a small amount of non-host data (a.k.a. metadata) for system managing purposes. We demonstrate that the metadata information can be readily and efficiently utilized by polar codes, whereas such property is lacking in LDPC-based systems. With the help of the side information provided by metadata, the decoding capability of polar codes can be further enhanced with little or no modifications on the decoder side. Simulation results verify the performance improvement of metadata-based JSCC scheme, and indicate that polar codes have competitive advantages over LDPC codes on flash memories.