Multistage decoding of multilevel block M-PSK modulation codes and its performance analysis

In this paper a coded modulation method for the additive white Gaussian noise channel is presented which incorporates signal shaping. The scheme uses a modulation map to map bits to channel inputs. A modulation map is considered that has the advantage it is can easily be combined with binary error-correcting codes. The decoding strategy is a combination of bit-interleaved coded modulation and multistage decoding. The number of required decoding stages is only small compared to other multistage decoding schemes for coded modulation. It is shown that modulation maps can be designed with a constrained capacity limit very close to the capacity of the AWGN channel. When combined with low-density parity-check codes, simulation results show that a near-capacity performance is achieved for high spectral efficiencies.

In this paper, we deal with the design of high rate multilevel two-dimensional (2D) bar codes for the print-and-scan channel. Firstly, we derive an upper bound on the maximum achievable rate of these codes by studying an inter-symbol interference (ISI) free, perfectly synchronized, and noiseless print-and-scan channel, in which the printer device uses halftoning in order to simulate multiple gray levels. Secondly, we present a new model of the print-and-scan channel specifically adapted to the multilevel 2D bar code application. This model, inspired by our experimental work, assumes no ISI and perfect synchronization, but independence between the channel input and the noise is not required. For completeness, we briefly review three state-of-the-art coded modulation techniques for the additive white Gaussian noise channel in the high signal-to-noise ratio regime, namely, multilevel coding with multistage decoding (MLC/MSD), multilevel coding with parallel independent decoding, and bit-interleaved coded modulation. We then derive the information capacity of our print-and-scan channel model and extend the theory of MLC/MSD to this channel. Finally, we present experimental results confirming the validity of our channel model, and showing that multilevel 2D bar codes using MLC/MSD can reliably achieve the high rate storage requirements of many multimedia security and data management applications.

Motivated by recent results in Joint Source/Channel (JSC) coding and decoding, this paper addresses the problem of soft input decoding of Arithmetic Codes (AC). A new length-constrained scheme for JSC decoding of these codes is proposed based on the Maximum a posteriori (MAP) sequence estimation criterion. The new decoder, called Chase-like arithmetic decoder is supposed to know the source symbol sequence and the compressed bit-stream lengths. First, Packet Error Rates (PER) in the case of transmission on an Additive White Gaussian Noise (AWGN) channel are investigated. Compared to classical arithmetic decoding, the Chase-like decoder shows significant improvements. Results are provided for Chase-like decoding for image compression and transmission on an AWGN channel. Both lossy and lossless image compression schemes were studied. As a final application, the serial concatenation of an AC with a convolutional code was considered. Iterative decoding, performed between the two decoders showed substantial performance improvement through iterations.

Motivated by recent results in Joint Source/ Channel (JSC) coding and decoding, this paper addresses the problem of soft input decoding of Arithmetic Codes (AC). A new length-constrained scheme for JSC decoding of these codes is proposed based on the Maximum a posteriori (MAP) sequence estimation criterion. The new decoder, called Chase-like arithmetic decoder is supposed to know the source symbol sequence and the compressed bit-stream lengths. First, Packet Error Rates (PER) in the case of transmission on an Additive White Gaussian Noise (AWGN) channel are investigated. Compared to classical arithmetic decoding, the Chase-like decoder shows significant improvements. Results are provided for Chase-like decoding for image compression and transmission on an AWGN channel. Both lossy and lossless image compression schemes were studied. As a final application, the serial concatenation of an AC with a convolutional code was considered. Iterative decoding, performed between the two decoders showed substantial performance improvement through iterations.

A novel construction of lattices is proposed. This construction can be thought of as a special class of Construction A from codes over finite rings that can be represented as the Cartesian product of $L$ linear codes over $\mathbb {F}_{p_{1}},\ldots ,\mathbb {F}_{p_{L}}$ , respectively, and hence is referred to as Construction $\pi _{A}$ . The existence of a sequence of such lattices that is good for channel coding (i.e., Poltyrev-limit achieving) under multistage decoding is shown. A new family of multilevel nested lattice codes based on Construction $\pi _{A}$ lattices is proposed and its achievable rate for the additive white Gaussian noise channel is analyzed. A generalization named Construction $\pi _{D}$ is also investigated, which subsumes Construction A with codes over prime fields, Construction D, and Construction $\pi _{A}$ as special cases.

Our objective is to design efficient coded modulation techniques with multi-stage decoding (MSD) for Rayleigh fading channels. The well-known rate design rule is conventionally used for AWGN channels. We extend the application of the rate design rule for multi-level coding by considering MSD for Rayleigh fading channels with interleaving. We model the fading channel as a time invariant additive non-Gaussian noise channels by assuming that the perfect channel state information is available at the receiver. The equivalent channel capacity curves that can be used for the multi-level code design for Rayleigh channels, and a code design example are presented. We demonstrate that a very good coding gain can be achieved if code rates are selected correctly.

The achievable information rates for multilevel coding (MLC) systems with multistage decoding (MSD) are examined on two-dimensional binary-input intersymbol interference (ISI) channels. One MSD scheme employs trellis-based detection, while another involves zero-forcing equalization and linear noise prediction. Information rates are determined by examining the output statistics at each stage of MSD. The first scheme is shown to achieve rates very close to known information-theoretic limits. Systems with low-density parity-check codes are then optimized to approach these rates

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.

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.

The Gaussian modulated continuous variable quantum key distribution (GM-CVQKD) protocol is known to maximise the mutual information between two parties during quantum key distribution (QKD). An alternative modulation scheme is the discrete modulated CVQKD (DM-CVQKD) protocol. In this paper, we perform a feasibility study for practical satellite-to-ground CVQKD with a focus on comparing existing GM-CVQKD and DM-CVQKD protocols with the application of the performance of recent reconciliation methods. We use a satellite-to-ground link model which takes into account geometric losses, scintillation, and scattering losses from the link distance, atmospheric turbulence, and atmospheric aerosols, respectively. In addition, recent multidimensional (MD) and multilevel coding and multistage decoding (MLC-MSD) reconciliation method models in combination with multiedge-type low-density parity-check (MET-LDPC) code models have been used to determine the reconciliation efficiency. Realistic parameters have been used for the calculation of the secret key rate (SKR) along with a comparison between MD and MLC-MSD reconciliation during satellite-to-ground GM-CVQKD, for the first time. The results show that GM-CVQKD outperforms DM-CVQKD. In addition, GM-CVQKD with MD reconciliation outperforms GM-CVQKD with MLC-MSD reconciliation in the finite size limit by producing positive SKRs at larger link distances and lower elevation angles.

A simple sphere bound gives the best possible tradeoff between the volume per point of an infinite array L and its error probability on an additive white Gaussian noise (AWGN) channel. It is shown that the sphere bound can be approached by a large class of coset codes or multilevel coset codes with multistage decoding, including certain binary lattices. These codes have structure of the kind that has been found to be useful in practice. Capacity curves and design guidance for practical codes are given. Exponential error bounds for coset codes are developed, generalizing Poltyrev's (1994) bounds for lattices. These results are based on the channel coding theorems of information theory, rather than the Minkowski-Hlawka theorem of lattice theory.

The concatenation scheme MLC-STBC combining multilevel codes (MLC) and space-time block codes (STBC) is proposed over Rayleigh fading channels. Through performance analysis and computer simulation, the asymptotic behavior of the new system is provided, which is proportional to the product of the space diversity and the minimum Hamming distance of the component codes. The simulation results show that, with the same bandwidth efficiency, the concatenation scheme has better power efficiency than the MLC system. Considering the fact that multistage decoding (MSD) and parallel decoding on levels (PDL) have a little difference in the system performance, the concatenation scheme MLC-STBC with PDL decoding method (MLC-STBC/PDL) achieves better trade-off between performance and complexity.

This paper investigates linear precoding for bit-interleaved coded modulation (BICM) on additive white Gaussian noise (AWGN) channels. Concatenating a linear precoder as an inner encoder with an outer (convolutional) encoder produces a powerful code with a limited decoding complexity. Linear precoders are examined and optimized for two scenarios: using (i) a noniterative decoding strategy and (ii) an iterative decoding strategy under a perfect feedback assumption. The precoder design is based on an information-theoretical approach, on the one hand, and a pair-wise error probability (PEP) analysis, on the other hand. Both approaches render convenient precoder design rules. For a binary phase-shift keying (BPSK) signal set, the optimal precoders that result from these rules are also derived. Numerical results confirm the analytical findings and simulations illustrate the effectiveness of the approach.

SummaryThis paper has deeply investigated the performance signature of modulation techniques based low earth orbit (LEO)/medium earth orbit (MEO) intersatellite optical wireless communication systems for possible communication coverage distance of 20 000 km with possible transmission bit rate of 0.5 Tb/s. These modulation techniques that are namely multilevel quadrature amplitude modulation (M‐QAM), multilevel phase shift keying (N‐PSK), multilevel pulse amplitude modulation (H‐PAM), and finally multilevel differential phase shift keying (L‐DPSK) based on different electrical pulse generators for upgrading LEO/MEO intersatellite link operation efficiency. These pulse generators that are namely Gaussian pulse generator (GPG), hyperbolic secant pulse generator (HSPG), and raised cosine pulse generator (RCPG). The variations of maximum Q‐factor, minimum bit error rate (BER), and optical signal‐to‐noise ratio in relation to number of bits/symbol for different modulation techniques can be deeply studied in the presence of vertical cavity surface emitting laser (VCSEL). This study is done with using Optiwave system simulation version 7 for different modulation techniques, and all figures are sketched with using wizard Excel sheet set up. It is observed that maximum Q‐factor and minimum BER are optimized with using GPG and 8‐PAM, as well as 4‐DPSK with both HSPG and RCPG.

Motivated by the capacity-approaching property of both binary polar codes (PCs) and the multi-level coding (MLC) scheme, we consider the design of modulated PC over additive white Gaussian noise (AWGN) channels. The capability of modulated PC essentially depends on the selection of information bits set from all the virtual bit channels formed by both modulation and channel polarization. To this end, we characterize the a priori distribution density as the sufficient statistic for the bit channel of individual modulation levels formed by an MLC scheme, in which the codeword of symbols is split into parallel bits streams. According to the factor graph generated by the binary PC, we apply the density evolution (DE) for each binary modulation level. Consequently, distribution densities of every bit within the modulated codeword can be obtained and we select the most reliable bits as information bits and set the complement as frozen bits. Comprehensive simulations demonstrate the validness of this approach compared to the benchmark scheme.