A non-volatile memory system may be configured to generate a codeword with first-type parity bits and one or more second-type parity bits. If a storage location in which the codeword is to be stored includes one or more bad memory cells, the bit sequence of the codeword may be arranged so that at least some of the second-type parity bits are stored in the bad memory cells. During decoding, a first set of syndrome values may be determined for a first set of check nodes and a second set of syndrome values may be determined for a second set of check nodes. In some examples, a syndrome weight used for determining if convergence is achieved may be calculated using check nodes that are unassociated with the second-type parity bits.