Iterative detection and decoding for separable two-dimensional intersymbol interference

We introduce two detection methods for uncoded two-dimensional (2-D) intersymbol interference (ISI) channels. The detection methods are suitable for a special case of 2-D ISI channels where the channel response is separable. In this case, the 2-D ISI is treated as the concatenation of two one-dimensional ISI channels. The first method uses equalization to reduce the ISI in one of the two dimensions followed by use of a maximum a posteriori (MAP) detector for the ISI in the other dimension. The second method employs modified MAP algorithms to reduce the ISI in each dimension. The implementation complexity of the two methods grows exponentially in the ISI length in either the row or column dimension. We develop two iterative decoding schemes based on these detection methods and low-density parity-check codes as error correction codes. Simulation results show that the bit-error-rate performance loss caused by the 2-D ISI for the separable channel response considered is less than 1 dB over a channel without ISI. This motivates equalizing a general 2-D ISI channel response to a nearby separable matrix.