Multimode two-dimensional balanced conservative codes for holographic storage

Multimode coding is a promising coding method owing to the simplicity of its code design and the attainment of high code rate. The authors present a multimode coding scheme for generating two-dimensional balanced t-conservative arrays for holographic storage. The multimode encoding process involves adding each unconstrained input array to a set of control arrays to form the selection set and selecting a pseudo-balanced t-conservative array from the selection set. By appropriately encoding the indices of the control arrays and using the remaining bits in the extra column or row appended to the selected pseudo-balanced t-conservative array to jointly balance the entire encoded array and to ensure that the extra column or row contains a sufficient number of transitions, the final output of the multimode encoder satisfies both the balanced and the t-conservative constraints. The decoding process is straightforward given the knowledge of the control array that was applied to the input array during the encoding process.