determined given a fixed value for g and original modulations d m to decode the grassmann constellations the glrt process provides the maximum likelihood ml performance because of the codeword orthogonality by searching for the maximum squared norm over the sub space codeword projection of the l symbol received signal block as follows max m u2062 uf605 r u2061 kl 1 u2026 r u2061 kl l u2062 g m h uf606 2 where u2225 u2225 denotes the euclidean norm because x y polarization signals are mutually orthogonal the glrt process obtains the ml estimate of the transmitted data regardless of any polarization crosstalk hence crosstalk cancellations and channel estimations are not necessary at the receiver for any depolarized fiber channels the performance is improved with multi block decoding with high order glrt although the grassmann constellation achieves near capacity performance when the block length goes to infinity it becomes hard to optimize all the constellation points for a large cardinality the minimum allowable block length for grassmann constellations is l 4 for which the cardinality becomes more than 65 thousand to achieve 2 bits per second per polarization as shown in fig3 as an alternative approach which reduces the cardinality the embodiments of invention provide a method 300 to make a full use of unitary constellations which allow differential encoding for 2 u00d7 2 dimensional modulations as an example of unitary constellations the m th codeword u m 312 of the unitary code set u 311 is given by the following form u m u2147 j u2062 2 u2062 u03c0 u2062 u2062 m m 0 0 u2147 j u2062 u2062 2 u2062 u03c0 u2062 u2062 m u2062 u2062 k 1 m u2061 cos u2061 2 u2062 u03c0 u2062 u2062 m u2062 u2062 k 2 m sin u2061 2.