This letter describes how to improve performance of OFDM systems by combining non-equiprobable signaling with low density parity check (LDPC) coding. We partition a standard QAM constellation into annular subconstellations of equal size, and we implement non-equiprobable signaling through a shaping code which selects subconstellations with large average energy less frequently than subconstellations with small average energy. In equiprobable signaling, the LDPC code selects a signal point from the inner subconstellation. In non-equiprobable signaling this inner signal point has a representative in each subconstellation and the shaping code selects the representative for transmission. It is possible to use standard QAM constellations to achieve any desired fractional bit rate with this method of shaping the energy distribution of the transmitted signal. 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 present simulation results for non-equiprobable transmission at $1.5$ bits/symbol on a representative Veh-A channel showing gains of $4$ dB at a bit error rate (BER) of $10^{-3}$. As the transmission rate increases, the gains from non-equiprobable signaling diminish, but we show through simulation that they are still significant for $16$-QAM.

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