On non-linear space-time block codes

A number of space-time block codes have been proposed for the quasi-static, flat-fading channel with coherent receiver. All of these block codes are linear codes, i.e., the encoded codeword is a linear function of the input scalar symbols. Here we propose new non-linear space-time block codes, i.e., the codewords are non-linear functions of the input scalar symbols. We demonstrate a non-linear code that outperforms the corresponding linear code by 0.6 to 1.2 dB. We draw parallels between optimal non-linear code design and the well-known simplex conjecture for multidimensional AWGN codes. Finally we show that for certain non-uniformly distributed input symbols, the optimal signal set cannot be designed with linear modulation and non-linear modulation is essential for optimality. This has applications in the design of space-time trellis codes and concatenated space-time coding schemes.