Precoding and the MMSE-DFE

This paper provides upper and lower bounds on the information rates achievable with a minimum mean square error (MMSE) Tomlinson-Harishima precoder (THP) assuming ideal interleaving. We also give an exact formula for zero-forcing (ZF) THP achievable information rates. At high SNR, the performance of the MMSE-THP and the ZF-THP identically suffer only the 2.55 bit or 1.53 dB -shaping" loss from capacity. At low SNR, shaping loss is negligible, but the THP systems again do not achieve capacity, largely due to the receiver modulo operation (and interleaving in the MMSE case). In general, the MMSE-THP outperforms the ZF-THP at low SNR. We show these effects for an example ISI channel.<
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