The effect of channel side information at transmitter on coding complexity

For some channels, channel side information at the transmitter (CSIT) may not improve channel capacity. For example, for binary input and symmetric output memoryless channels, uniform input distribution is capacity achieving with or without CSIT. However, we show that CSIT can help reduce the complexity of codes if the code is designed using channel knowledge and provide for lower bounds on complexity. A code optimization problem for minimizing complexity for a given rate loss is also posed.