Coding Schemes for Energy Constrained IoT Devices

In this paper, we investigate the ultimate performance limits, in terms of achievable information rate (IR), of communication systems impaired by impulse noise. We compare single carrier (SC) and multi-carrier (MC) transmission systems employing quadrature amplitude modulation (QAM) formats. More precisely, we consider SC schemes with coded modulations and MC systems based on orthogonal frequency division modulation (OFDM). For the MC schemes, we introduce a theoretically equivalent channel model which makes the computation of the IR feasible. This simple channel model will be referred to as interleaved MC. We show that, in the presence of impulse noise and except for systems operating at very high spectral efficiency, the IR of MC schemes is lower than that of SC schemes. More precisely, use of MC schemes may lead to an unavoidable fundamental loss with respect to SC schemes at typical coding rates, whereas MC schemes are to be preferred for very high coding rates or in uncoded systems. These results hold for additive white Gaussian noise (AWGN) and dispersive channels, either considering plain OFDM or MC schemes employing water-filling and bit-loading algorithms. In order to validate our theoretical results, we also obtain the bit error rate (BER) performance of SC and MC schemes through Monte Carlo simulations. A few trellis-coded modulation (TCM) and low-density parity-check (LDPC)-coded schemes are considered. The obtained SNR loss in the BER curves between the AWGN and impulse noise channels matches well with the corresponding IR gap.

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.

This paper investigates an iterative multiuser detection for nonbinary low density parity check (LDPC) coded multicarrier multiple level frequency shift keying system to increase system performance under specific signal-to-noise ratio and data rate. We propose three-level hard-limited detection probabilities over both additive white Gaussian noise (AWGN) channels and Rayleigh fading channels. During multiuser detection (MUD) process, the hard-limited detection probabilities are computed in advanced and stored in tables. By using table looking up, the MUD soft outputs can be computed efficiently. We test the reliability of soft outputs from nonbinary LDPC channel decoder for all users. If the soft output exceeds a reliability threshold, the user is declared as a reliable user. For each symbol, we count the number of reliable users on it, and, use this information to update the soft output of MUD during the iterative multiuser detection and decoding process, which cancel multiple access interference iteratively. Numerical results show that the performances of three-level hard-limited systems outperform two-level hard-limited systems over AWGN channels and Rayleigh fading channels.

Low-density parity checks (LDPC) codes are considered good performance error correction codes. However, decoder complexity increases with increasing code length. In this study, we introduce short-length serially concatenated LDPC codes. The proposed technique uses pairs of compatible LDPC codes that act as outer and inner serially concatenated codes. In this code pair, the inner code takes input that is the same length as the outer LDPC encoder output. This study examined two cases of LDPC codes as compatible pairs with low numbers of iterations and compared bit error rate (BER) performance to a standalone LDPC code with an additive white Gaussian noise channel. We also considered the quadrature phase shift keying QPSK, 16-quadrature amplitude modulation (QAM), and 64-QAM system modulation schemes. Simulation results demonstrate that the proposed system has good BER performance compared to a standalone LDPC code, the results summarized in table and performance curves.

Recently, the differential detection scheme has attracted considerable attention as a demodulated scheme for digital mobile communications because of its robustness in the frequency nonselective fading channel. A problem of the differential detection scheme is that its bit error rate (BER) performance in the additive white Gaussian noise (AWGN) channel is inferior to that of the coherent detection scheme. To solve this problem, many methods to improve BER performance of the differential detection in the AWGN channel have been proposed. However, those methods require complex signal processings.This paper proposes a novel differential detection scheme as a simpler improvement method which estimates the differential phase of the transmitted signal by a sequence estimation scheme using the Viterbi algorithm. The proposed scheme is simplified in a manner such that its signal processing is composed of only additions and subtractions on the phase information of the received signal. Results of computer simulation show that BER performance of the proposed scheme is close to that of the ideal coherent detection in the AWGN channel. In addition, the trellis diagram of the Viterbi algorithm can be reduced without performance degradation introducing the signal processing similar to the Scarece State Transition (SST) type Viterbi decoding. The proposed scheme also is useful in the case of the fast Rician fading channel and the slow Rayleigh fading channel.

The optical ZCZ code, which is a set of pairs of binary and biphase sequences with zero correlation zone, can provide code division multiple access (CDMA) communication system without co-channel interference. The M-ary amplitude shift keying spread spectrum (M-ary/ASK-SS) system using this code can detect a desired sequence without interference of undesired sequences. We have proposed the compact construction of a matched filter bank for this code, which is called the compact-type matched filter bank. However, M-ary/ASK-SS system using this filter bank might go down the bit error rate (BER) performance because input-output characteristics of this filter bank for this code with zero correlation zone 4n - 2 are nonlinear characteristics. In this paper, we clarify that BER performance in the M-ary/ASK-SS system over the additive white Gaussian noise (AWGN) channels is not influenced by nonlinear characteristics of this filter bank by the theoretical formula of BER characteristics and the computer simulation. The BER performance in the ASK-SS system using compact-type matched filter under the AWGN environment go down compared to that using direct-type matched filter as expected. But the BER performance in the M-ary/ASK-SS system using this compact-type matched filter bank under the AWGN environment is almost equal compared to that using parallel-type matched filter bank. In fact, this compact-type matched filter bank is effective in the M-ary/ASK-SS system.

In this paper, a novel coded modulation scheme named Trellis-Coded Differential Chaotic Modulation (TC-DCM) is proposed, which combines trellis codes with M-ary Differential Chaotic Shift Keying (M-DCSK). The new scheme not only reduces the multipath interference efficiently due to its inherent spreading property, but also avoids the use of Channel State Information (CSI), exact synchronization, despreading and the Rake receiver, making the corresponding receiver design simpler and more suitable for band-limited communication systems under severe multipath propagation conditions. Analytical Bit-Error-Rate (BER) bounds are derived and verified over Additive White Gaussian Noise (AWGN) channels. Both analytical performances and simulation results show that the proposed scheme with different states and different coding rates can obtain significant coding gains, compared to the corresponding uncoded schemes with the same bandwidth over AWGN channels. In addition, it is found from simulations that over multipath Rayleigh fading channels without CSI, the proposed TC-DCM system outperforms the Trellis-Coded Modulation Direct-Sequence Spread-Spectrum (TCM DS/SS) system with the same bandwidth efficiency.

This paper examines the bit error rate (BER) of a direct sequence spread spectrum (SS) system that uses bandlimited white Gaussian noise (BLWGN) as a spreading code. The performance of this bandlimited-SS system is examined in both additive white Gaussian noise (AWGN) and single tone jamming environments. The BLWGN spreading code is inferior to conventional codes in AWGN channels, but is more robust when a narrow band interference signal is present.

The Orthogonal Frequency Division Multiplexing (OFDM) is also known as multicarrier technology. Wideband digital communications in the recent past have increasingly utilized OFDM. It can withstand difficult channel circumstances, efficiently utilize spectrum resources, decrease ISI, and operate at a high data rate, among many other benefits. It has been used in several wireless and wired communication systems, including fourth generation Long-Term Evolution (4G LTE) mobile communications. The performance assessment and analysis of the OFDM system under Additive White Gaussian Noise (AWGN) channel has been carried out in this work. The factors in which system performance is assessed include the signal quality, Bit Error Rates (BERs), and Signal to Noise Ratios (SNRs) of the received signals. To improve performance while employing multicarrier modulation, the subcarriers must be kept orthogonal to one another, in the process known as OFDM. The sole focus of this study is the performance analysis of PAPR, BER, and SNR utilizing various modulation methods and schemes.

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.

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.

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.

This paper presents asymptotic multiuser efficiency (AME) performance analysis of the decorrelator based successive interference cancellation (DBSIC) DS-CDMA multiuser receiver DBSIC is similar to the conventional SIC receiver except that a decorrelator is used at each detection stage prior to cancellation. AMEs of DBSIC are compared with those of single-user matched filter, optimum, decorrelating and conventional SIC receivers over both additive white Gaussian noise (AWGN) and Rayleigh fading channels. It is shown that over AWGN channels, DBSIC AME is lower than the optimum receiver AME when the interfering user is weaker than the user of interest but approaches the unity optimum receiver AME as the interferer becomes stronger than the user of interest. For all spreading codes cross-correlation considered, DBSIC has a similar AME curve shape as the conventional SIC receiver but has a higher AME which remains positive for all user energy ratios, illustrating its near-far resistance over AWGN channels. The AME of DBSIC is better than that of the decorrelating detector when the interferer is much weaker or slightly stronger than the user of interest and has worse performance when the interferer is not much weaker. It is shown that DBSIC is completely near-far resistant over Rayleigh fading channels with the same AME as the decorrelating scheme for user 1 and as the optimum scheme for user 2, both AMEs being independent of the user energy ratio. This shows that DBSIC is preferable compared to the decorrelating detector, while still being less complex than the optimum scheme over Rayleigh fading channels

This correspondence analyzes the performance of concatenated coding systems and modulation schemes operating over the additive white Gaussian noise (AWGN) channel by examining the loss of capacity resulting from each of the processing steps. The techniques described in this correspondence allow the separate evaluation of codes and decoders and thus the identification of where loss of capacity occurs. Knowledge of this capacity loss is very useful for the overall design of a communications system, e.g., for evaluating the benefits of inner decoders that produce information beyond the maximum-likelihood (ML) estimate. The first two sections of this correspondence provide a general technique for calculating the composite capacity of an orthogonal or a bi-orthogonal code and the AWGN channel in isolation. The later sections examine the composite capacities of an orthogonal or a bi-orthogonal code, the AWGN channel, and various inner decoders including the decoder estimating the bit-by-bit probability of a one, as is used in turbo codes. The calculations in these examples show that the ML decoder introduces a large loss in capacity. Much of this capacity loss can be regained by using only slightly more complex inner decoders, e.g., a detector for M-ary frequency-shift keying (MFSK) that puts out the two most likely frequencies and the probability the ML estimate is correct produces significantly less degradation than one that puts out only the most likely frequency.

Modulo lattice additive noise (MLAN) channels appear in the analysis of structured lattice codes with lattice decoding for Costa's dirty-paper channel and the additive white Gaussian noise (AWGN) channel. Building on the recent result on the optimal density of an infinite constellation over an AWGN channel, in this paper, it is shown that with a proper choice of the shaping lattice and the scaling parameter, the dispersion of the MLAN channel is asymptotically the same as that of the (zero-interference) AWGN channel at the same signal-to-noise ratio.