We present an algorithm for computing the communication sets in array section movements with block-cyclic (cyclic(k) in HPF) distribution. Our framework can handle multi-level alignments, multi-dimensional arrays, array intrinsic functions, affine indices and axis exchanges in the array subscript. Instead of employing the linear diophantine equation solver, a new algorithm which does not rely on the linear diophantine equation solver to calculate communication sets is proposed We use formal proof and experimental results to show that it is more efficient than previous solution to the same problem. Another important contribution of the paper is that we prove that the compiler is able to compute efficiently the communication sets of block-cyclic distribution as long as the block sizes of the arrays are set to be identical or the lowest common multiple (LCM) of block sizes is not a huge integer We demonstrate it by thorough complexity analyses and extensive experimental results.