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We introduce partial response maximum likelihood (PRML) with the two-dimensional (2D) soft output Viterbi algorithm (SOVA) and 2D equalizer for holographic data storage (HDS) channel. The 2D SOVA output is the average of two 1D SOVAs that are separately operated in horizontal and vertical directions. The complexity of the proposed 2D SOVA is increased only twice compared with 1D SOVA while its performance is superior to that of 1D SOVA. Since the 2D SOVA outputs soft decision value, LDPC can be utilized by the soft-in hard-out decoding. We study for different PR target, comparing 1D Viterbi detection with 2D SOVA detection, different misalignments, and two kinds of LDPC codes.