Oversampling for Colored Noise ISI Channels

We derive the channel capacity of colored noise ISI channels by the mutual information of a block based model, where we assume that the receiver samples the received signal at the rate higher than the symbol rate and the receiver detects each block on the basis of the received samples over the channel length. We derive a condition for eliminating the effect of inter-block ISI (IBI) and show that the IBI-free information rate can reach the channel capacity when unit block length (where the block length is equal to one symbol period) is employed. In addition, we show that colored noise channel capacity can be larger than white noise channel capacity. To realize the theoretical results, we further propose oversampling based block detection. We show that the achievable rate for oversampling based block detection is equal to the information rate for the block based model. We also show that oversampling based block detection with unit block length is equivalent to oversampling based combining. This result implies that the achievable rate for oversampling based combining can reach colored noise channel capacity.