Levinson Recursion for Tall (Non Square) Toeplitz Matrices

Question

Given a tall non square Toeplitz Matrix $ H $, how could one solve:

$$ y = H x $$

In the general case it would be generated by (MATLAB Code):

numRows = 10; %<! Or any other number
numCols = 20; %<! Or any other number larger than 'numCols'
vR = randn(numRows, 1);
vC = randn(numCols, 1);
mH = toeplitz(vC, vR);

Since the Matrix is tall (Not square), I'm after the least squares solution:

$$ \arg \min_{x} {\left\| H x - y \right\|}_{2}^{2} $$

I have implemented the Levinson Recursion for the square case yet I'd like to know if there is an extension to it for the case the Toeplitz matrix isn't square.