Advanced GF(3^2) nonbinary LDPC coded modulation with non-uniform 9-QAM outperforming star 8-QAM

Abstract

Abstract:In this paper, we first describe a 9-symbol non-uniform signaling scheme based on Huffman code, in which different symbols are transmitted with different probabilities. By using the Huffman procedure, prefix code is designed to approach the optimal performance. Then, we introduce an algorithm to determine the optimal signal constellation sets for our proposed non-uniform scheme with the criterion of maximizing constellation figure of merit (CFM). The proposed nonuniform polarization multiplexed signaling 9-QAM scheme has the same spectral efficiency as the conventional 8-QAM. Additionally, we propose a specially designed GF(3 2 ) nonbinary quasi-cyclic LDPC code for the coded modulation system based on the 9-QAM non-uniform scheme. Further, we study the efficiency of our proposed non-uniform 9-QAM, combined with nonbinary LDPC coding, and demonstrate by Monte Carlo simulation that the proposed GF(2 3 ) nonbinary LDPC coded 9-QAM scheme outperforms nonbinary LDPC coded uniform 8-QAM by at least 0.8dB. Peckham, "Coded PDM-OFDM transmission with shaped 256-iterative-polar-modulation achieving 11.15-b/s/Hz intrachannel spectral efficiency and 800-km reach," J. Lightwave Technol. 31(4), 538-545 (2013).

Temporal Probabilistic Shaping for Mitigation of Nonlinearities in Optical Fiber Systems

“…[16]) 3 . Different merging criteria are therefore needed in order to increase the order of the FSMS while retaining the complexity and preserving the shaping gains from Fig.…”

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

“…Combining Equations (11) and (12), and denoting the probability of correct decision for signal point '0' using P 0 , it could be written 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.…”

Performance analysis of hybrid geometric-probabilistic shaped 8/12 quadrature amplitude modulation for coherent optical communication system

“…9 In addition, the low-energy transmitted points with large probabilities suffer less fiber nonlinear effects. 10 Considering the performance advantages of GS and PS, hybrid shaping (HS) can achieve a larger shaping gain, reduce the BER, and further approach the Shannon limit; thus it has drawn extensive attention. [11][12][13] A HS 14 scheme based on the generalized pairwise optimization algorithm was proposed.…”

“…More symbols were mapped to low-energy points and fewer symbols were mapped to high-energy points 9 . In addition, the low-energy transmitted points with large probabilities suffer less fiber nonlinear effects 10 . Considering the performance advantages of GS and PS, hybrid shaping (HS) can achieve a larger shaping gain, reduce the BER, and further approach the Shannon limit; thus it has drawn extensive attention 11 …”