This letter describes how to improve performance of cellular systems by combining non-equiprobable signaling (shaping) with low-density parity check (LDPC) coding for an orthogonal frequency division multiplexing system. We focus on improving performance at the cell edge, where the 5G standard specifies a suite of LDPC codes with different rates that are applied to 4-QAM. We employ the method of shaping on rings which adds to the transmission rate as it shapes the input distribution. We double the size of the $4$-QAM constellation by introducing a second shell of signal points, and we implement non-equiprobable signaling through a shaping code which selects the high energy shell less frequently than the low energy shell. We describe how to combine coding and shaping by integrating shaping into the calculation of log-likelihood ratios (LLRs) necessary for decoding LDPC codes. We employ rate $1/2$ LDPC coding and select the rate of the shaping code to match that of rate $3/4$ LDPC coding using $4$-QAM. We present simulation results for a representative Veh-A channel showing gains of $4$ dB at a bit error rate (BER) of $10^{-3}$. When we choose an LDPC code from the 5G suite to match the BER performance of rate $1/2$ LDPC coding with shaping we show that transmission rate can be improved by $20 $%.

翻译：本文描述如何通过将非等概率信号传输（成形）与低密度奇偶校验编码相结合，以提升正交频分复用系统在蜂窝网络中的性能。我们重点关注小区边缘的性能改进，该场景下5G标准规定了一套适用于4-QAM、具有不同码率的LDPC编码方案。我们采用环形成形方法，通过塑造输入分布来提升传输速率。通过引入第二层信号点，我们将$4$-QAM星座的规模扩大一倍，并借助成形编码实现非等概率信号传输，使得高能量层的选择频率低于低能量层。我们阐述了如何通过将成形技术整合到解码LDPC码所需的对数似然比计算中，实现编码与成形的联合优化。采用码率$1/2$的LDPC编码，并选择与使用$4$-QAM的码率$3/4$ LDPC编码相匹配的成形编码率。针对典型Veh-A信道的仿真结果表明，在误码率为$10^{-3}$时可获得$4$ dB的性能增益。当我们从5G标准编码集中选取LDPC码，使其误码率性能与采用成形的码率$1/2$ LDPC编码相当时，传输速率可提升$20\%$。