Abstract: A data storage system includes a memory circuit having memory cells and a control circuit. The control circuit is operable to receive data bits provided for storage in the memory cells. A subset of the memory cells have predetermined stuck-at faults. The control circuit is operable to compute a binomial coefficient for each of the predetermined stuck-at faults based on a bit position of a corresponding one of the predetermined stuck-at faults within the memory cells. The control circuit is operable to add together the binomial coefficients to generate an encoded number using a combinatorial number system. The control circuit is operable to generate a first set of redundant bits that indicate the encoded number. The first set of redundant bits are used to decode bits read from the memory cells to regenerate the data bits.

Abstract: A data storage system has a memory circuit that comprises memory cells and a control circuit that receives data bits provided for storage in the memory cells. The control circuit encodes the data bits to generate a first set of redundant bits and encoded data bits, such that the encoded data bits selected for storage in a first subset of the memory cells with first stuck-at faults have digital values of corresponding ones of the first stuck-at faults. The control circuit encodes the first set of redundant bits to generate a second set of redundant bits. The control circuit performs logic functions on the second set of redundant bits and the encoded data bits to generate a third set of redundant bits, such that redundant bits in the third set of redundant bits selected for storage in a second subset of the memory cells with second stuck-at faults have digital values of corresponding ones of the second stuck-at faults.

Abstract: A data storage system includes a memory circuit that has memory cells and a control circuit that is operable to receive data bits provided for storage in the memory cells. The control circuit is operable to receive a first matrix. Each row of the first matrix corresponds to a unique one of the data bits. The control circuit is operable to generate a second matrix having only the rows of the first matrix that correspond to the data bits provided for storage in a subset of the memory cells having stuck-at faults. The control circuit is operable to generate a third matrix having linearly independent columns of the second matrix. The control circuit is operable to encode the data bits to generate encoded data bits and redundant bits using the third matrix.