Precoding and shaping for general signal-to-noise ratios

We design a combined signal shaping and channel coding scheme that can operate close to the Gaussian capacity limit at any signal-to-noise ratio in the presence of known interference. This is accomplished by using methods from multidimensional quantization and trellis shaping, building on previous results for the low spectral efficiencies. By computing mutual information limits based on extrinsic information transfer curves, we show that for low signal-to-noise ratio MMSE scaling combined with joint decoding of shaping and channel code is required to approach capacity, whereas for high signal-to-noise ratio the problem is reduced to classic sign-bit shaping, where separate decoding of sign-bit and unsigned bits suffices. For all signal-to-noise ratios we use repeat-accumulate codes to approach capacity, and offer guidelines for the performance/complexity trade-off at different SNRs.