Embedded method for indexing control arrays in multimode conservative codes for holographic storage

In multimode conservative codes for holographic storage, an unconstrained m times n binary array S of source data is added to a set of (m+1)(n+1) control arrays to form the selection set, which is guaranteed to contain at least one conservative array of strength at least t, such that each row and each column of the output array contain at least t transitions. To be able to retrieve the original source data array S during the decoding process, at least lceillog₂(m+1)(n+1)+ redundant bits are necessary to index the (m+1)(n+1) control arrays. Presented is a method for embedding the index information of the control arrays into the encoded arrays in a manner which requires only +log₂(m+1)+++log₂(n+1)+ redundant bits, thereby attaining high coding efficiency.