Computing cross-correlations on a quantum computer

Question

I am trying to compute cross-correlation on a quantum computer, and I have found a research paper describing the cross-correlation algorithm.
The terms used in the algorithm are not clear, and it would be great if someone can help me with it. The algorithm has many formating and special characters that I cannot copy and paste in the browser from the PDF.
The link to access the research paper is Cross-Correlations computation through quantum computing. On page number  4 the cross-correlation algorithm is mentioned.
I am not able to understand that in the second step of the algorithm, what is the j^ register, and what does it consist of?

DaftWullie · Answer

It is referring the the "function variable" register of figure 1. It consists of $log_2N$ qubits, all prepared in the $|0rangle$ state.

Computing cross-correlations on a quantum computer

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