Two classes of approximately universal codes are developed for parallel Gaussian channels whose state information is not available at the encoder. Both architectures convert the channel into a set of scalar additive white Gaussian noise (AWGN) channels to which good AWGN base codes can be applied, and both are layered schemes used in conjunction with successive interference cancellation to keep decoding complexity low. The first construction uses a concatenated code structure, and with perfect

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... ase codes achieves an arbitrarily high fraction of capacity in the limit of high SNR. The second construction uses a layer-dither-repeat structure, and with perfect base codes can achieve better than 90% of capacity at typical target spectral efficiencies, corresponding to a roughly 1 dB gap to capacity.