This paper proposes a new probabilistic amplitude shaping (PAS) approach for concatenated two-level multi-level coding (MLC). The proposed system is based on a concatenated forward error correction (FEC) scheme where outer codes are serially concatenated with inner two-level MLC. This concatenated two-level MLC scheme has recently been shown to have a potential for achieving better performance-complexity trade-offs than the conventional bit-interleaved coded modulation (BICM). Meanwhile, PAS has recently been demonstrated to offer remarkable performance gains as well as rate adaptivity. However, the majority of existing works on PAS assume the use of the binary reflected Gray code as a bit-labeling, and its application to coded modulation schemes with other bit-labelings, such as two-level MLC, may not be straightforward. In this paper, we devise a bit-labeling scheme and propose a new PAS structure for an efficient integration of PAS with two-level MLC systems. More specifically, we propose to generatesignedamplitude symbols with the distribution matcher (DM) for maximizing both coding and shaping gains achieved by two-level MLC and PAS, respectively, while the conventional PAS generatesunsignedamplitude symbols. It is demonstrated by simulation results that, with 256QAM and inner polar codes, the proposed two-level MLC with PAS simultaneously offers 75% reduction in the number of required inner encoding and soft-decision (SD) decoding operations for given outer and inner FEC code lengths, and up to 0.3 dB performance gain over the conventional PAS scheme.

We propose a new probabilistic amplitude shaping (PAS) scheme based on short linear block codes. In the proposed system, the capacity-approaching signal distribution is generated in the process of decoding linear block codes for a given information bit sequence. We associate the design problem of shaping codes with the classical covering problem, suggesting the use of good covering codes for shaping. From simulation results, it is demonstrated that by selectingperfectbinary codes as our shaping codes, the proposed scheme offers a shaping gain of around 0.3–1.0 dB. By comparing with the enumerative sphere shaping (ESS) of the same block length, we verify that the proposed scheme achieves significantly lower storage complexity and computational complexity at the receiver even with comparable block error rate performance.

In this paper, we propose a new polar coding scheme with molecular programming, which is capable of highly parallel implementation at a nano-scale without the need for electrical power sources. We designed chemical reaction networks (CRN) to employ either successive cancellation (SC) or maximum-likelihood (ML) decoding schemes for short polar codes. From differential equation analysis of the proposed CRNs, we demonstrate that SC and ML decoding achieve accurate computations across fully-parallel chemical reactions. In terms of the number of required chemical reactions, we verify the superiority of ML decoding over SC decoding for very short block lengths.

This paper studies a new application of deep learning (DL) for optimizing constellations in two-way relaying with physical-layer network coding (PNC), where deep neural network (DNN)-based modulation and demodulation are employed at each terminal and relay node. We train DNNs such that the cross entropy loss is directly minimized, and thus it maximizes the likelihood, rather than considering the Euclidean distance of the constellations. The proposed scheme can be extended to higher level constellations with slight modification of the DNN structure. Simulation results demonstrate a significant performance gain in terms of the achievable sum rate over conventional relaying schemes. Furthermore, since our DNN demodulator directly outputs bit-wise probabilities, it is straightforward to concatenate with soft-decision channel decoding.

Motivated by the recent advancement of quantum processors, we investigate quantum approximate optimization algorithm (QAOA) to employ quasi-maximum-likelihood (ML) decoding of classical channel codes. QAOA is a hybrid quantum-classical variational algorithm, which is advantageous for the near-term noisy intermediate-scale quantum (NISQ) devices, where the fidelity of quantum gates is limited by noise and de-coherence. We first describe how to construct Ising Hamiltonian model to realize quasi-ML decoding with QAOA. For level-1 QAOA, we derive the systematic way to generate theoretical expressions of cost expectation for arbitrary binary linear codes. Focusing on [7], [4] Hamming code as an example, we analyze the impact of the degree distribution in associated generator matrix on the quantum decoding performance. The excellent performance of higher-level QAOA decoding is verified when Pauli rotation angles are optimized through meta-heuristic variational quantum eigensolver (VQE). Furthermore, we demonstrate the QAOA decoding performance in a real quantum device.

The decoding of Construction D lattices is described. While similar to the multistage decoding of Code Formula codes, modification is required so that lattice components are subtracted in a process called reencoding. A generator matrix for Construction D lattices is given. Construction D lattices obtained from BCH codes were described by Barnes and Sloane. In this paper, we consider some practical issues of encoding and decoding these lattices. Using ordered statistics decoding, dimension 128 BCH code lattices outperform turbo lattices and low-density lattice codes of similar dimension. These results show relatively good performance of lattices based on algebraic constructions, compared to lattices typically designed for high dimensions. The performance over power-constrained channel is also evaluated, where the near-optimal performance is demonstrated.

In this paper, we develop capacity-approaching non- binary turbo codes defined over high-order finite fields. Since the performance of turbo codes is characterized by the convergence behavior of iterative decoding and error floor in the high SNR region, we attempt to design the non-binary turbo codes based on the following two-stage optimization processes: In the first stage, we employ a Gaussian approximation method for non-binary turbo codes and analyze the convergence property of iterative decoding. After reducing the search space by the first stage, the best component convolutional codes are identified by examining the truncated union bound under the assumption of the uniform interleaver. Simulation results demonstrate that our non-binary turbo codes as designed above can outperform the conventional non-binary LDPC codes.

In this paper, we present a new bandwidth-efficient coded modulation scheme based on parallel concatenation of the three component trellis coded modulation (TCM) encoders. The resulting triple parallel concatenated TCM (TPCTCM) is investigated for the spectral efficiency of 2 to 7 bits/sec/Hz based on two-dimensional (2-D) TCM employing PSK and QAM signal sets. The component code is designed based on the symbol-based three-dimensional (3-D) extrinsic information transfer (EXIT) charts. The simulation results in terms of frame error rate (FER) performance demonstrate that the proposed TPCTCM can significantly reduce the error floor of the conventional parallel concatenated TCM.