Embodiments of the invention provide a method of decoding of hexagonal constellations. The decoding methods exploit the inherent structure of the hexagonal grid to eliminate/minimize the requirements for distance computations. A constellation which has unused constellation points is received. A plurality of lookup tables is used for indicating whether a particular constellation point is used. The lookup tables are indexed using the two integers u and v. An initial estimate ū and v is found. The Euclidean distance to the immediate neighbors resulting in the immediate upper and lower integers for ū and v is computed. From the distance to the nearest neighbor, the log-likelihood ratio value is computed.