Increasing Data Rate through Shaping on Wireless Channels Subject to Mobility and Delay Spread

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 $%.

💡 Research Summary

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This paper investigates how to increase the data rate and improve the reliability of 5G NR transmissions at the cell edge by jointly applying non‑equiprobable (probabilistic) shaping and low‑density parity‑check (LDPC) coding within an orthogonal frequency‑division multiplexing (OFDM) framework. The authors focus on the scenario defined by the 5G NR standard where the cell‑edge uses 4‑QAM together with either a rate‑1/2 or a rate‑3/4 LDPC code. Because the rate‑3/4 code offers a 4 dB SNR advantage over the rate‑1/2 code at a BER of 10⁻³, the paper asks whether shaping can close this gap without increasing transmit power.

The proposed solution is “shaping on rings,” a probabilistic shaping technique that partitions a baseline 4‑QAM constellation into two concentric rings (inner low‑energy and outer high‑energy). By adding a second shell, the constellation becomes an 8‑point set (two points per label). A sparse shaping code of length z = 3 (e.g., the binary word