Tomlinson-Harashima Precoding

Tomlinson-Harashima Precoding is an equalization method done at the transmitter side. Consider a decision feedback equalizer (DFE) at the receiver. It usually consists of two filters: a feed forward filter and a feedback filter. These are usually implemented as FIR filters. The structure of a DFE is shown here:

This equalizer works very well if there is not an error correction coding with a significant coding gain in the system. If there is a need to such an error correction coding system, this means that there are many errors at the decision block output that need correction. The feedback filter part of a DFE only works correctly if the decision block output does not have many errors. The FBF actually tries to cancel what is called post-cursor ISI (inter symbol interference). This means that it assumes that previous decisions have been correct and uses those to remove the post cursor ISI. If many of the decisions of the decision block are erroneous, then the FBF not only cannot cancel the post cursor ISI, but it ads extra noise to the system. Which in turns causes more errors, and in this way the error at the output of decision block grows. This is called error propagation. To combat this one can move the FBF part of a DFE to the transmitter, as the result the system will look like this:

  

The "Modulo-M" block shown in the above figure makes sure that the output of THP stays in the range of (-M, +M] by adding appropriate integer multiple of 2M to the summation output. The reason that this block is there is to limit the signal level transmitted into the channel. Without it there will be some FBF coefficients that can make the output of summation point to large, which in many practical cases are not acceptable.

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