Diophantine approximation approach for incomplete decoding at relays

In this paper, we propose a low-complexity method to perform the incomplete decoding needed at relays for the incomplete decode-and-forward. The decoding problem is considered as a diophantine approximation search. We propose two modifications of Cassels´ algorithm to approximate an element x ¿ ???(i, ¿) by a linear combination a + ¿b of symbols taken in a Z-PAM. Simulation results show that the use of diophantine approximation induces only a small loss in performance, while reducing significantly the processing complexity.