Capacity achieving nonbinary LDPC coded non-uniform shaping modulation for adaptive optical communications

Abstract

A mutual information inspired nonbinary coded modulation design with non-uniform shaping is proposed. Instead of traditional power of two signal constellation sizes, we design 5-QAM, 7-QAM and 9-QAM constellations, which can be used in adaptive optical networks. The non-uniform shaping and LDPC code rate are jointly considered in the design, which results in a better performance scheme for the same SNR values. The matched nonbinary (NB) LDPC code is used for this scheme, which further improves the coding gain and the overall performance. We analyze both coding performance and system SNR performance. We show that the proposed NB LDPC-coded 9-QAM has more than 2dB gain in symbol SNR compared to traditional LDPC-coded star-8-QAM. On the other hand, the proposed NB LDPC-coded 5-QAM and 7-QAM have even better performance than LDPC-coded QPSK.

High-speed continuous-variable quantum key distribution over atmospheric turbulent channels

“…6. The reconciliation efficiency in use has been realized by the LDPC codes [21,22].The maximum SKR of >20 Mbit⁄s can be obtained when T=0.85, and V A = 0.35. We find that the SKR of >4 Mbit⁄s can be obtained when T=0.55, and the minimum transmittance of T= 0.35 is required to guarantee secure CV-QKD transmission.…”

Combination of High-Order Modulation and Non-Binary LDPC Codes over GF(7) for Non-Linear Satellite Channels

“…Finally, combining Equations (13) and (19), denoting the exact average SEP for the 7-QAM constellation using P 7-QAM , it can be expressed as…”

“…In addition, the combination of 8-PSK and low-density parity-check (LDPC) codes is a very popular candidate scheme for satellite communication system because of the robustness of 8-PSK against the non-linear distortion and the excellent error correction performance of the LDPC codes [11]. However, compared to other constellations, such as 8-QAM, 5-QAM, and 9-QAM presented in [12,13] and the general hexagonal constellation [14,15], 8-PSK only has a ring and wastes the space of little amplitude, which results in the poor anti-noise performance and the limitation for the error performance of this scheme. In [16], 5-QAM is used as the modulation method in the solution for the fifth-generation (5G) cellular networks.…”

End-to-end Learning for GMI Optimized Geometric Constellation Shape

“…Constellation shaping is now a well-established technique in the optical communications research community for improving the system throughput and operate close to the theoretically achievable information rate and at high spectral efficiency. Both probabilistic shaping [1][2][3] and geometric shaping [4,5,[10][11][12], each having its benefits and drawbacks, are of significant interest to both system vendors and researchers. Probabilistic shaping refers to optimizing the probabilities of the constellation points, typically applied to rectangular quadrature amplitude modulation (QAM), whereas geometric shaping refers to optimizing the positions of the constellation points.…”

“…Probabilistic shaping provides slightly higher shaping gains than geometric shaping in terms of the generalized mutual information (GMI), since non-rectangular constellations lack an obvious Gray-like code. This problem can be avoided, in trade-off for increased complexity, by employing Geometric shaping with iterative demapping and decoding [5], or with non-binary forward error correction (FEC) [4]. Also probabilistic shaping includes similar trade-off, as it requires a shaping encoder, such as the constant composition distribution matcher [3,6,7].…”