Based on the characteristic of multi-path frequency selective channel, the algorithm combines rapid table lookup and Lagrange-multiplier method to iteratively search the optimal bit allocation scheme.

By means of Lagrange multiplier method, this method distributes the slack to the operator nodes in the data path, thus, efficiently reduces the energy consumption of design circuit.

Then its generalized variational principle is established on the basis of Lagrange multiplier method by absorbing the first kind of boundary condition.