Constrained coding and soft iterative decoding for storage

Constrained coding, in which a certain restrictions known as a modulation constraint are placed on the sequence that can be transmitted through a digital communications channel is commonly used in magnetic and optical storage. Error-correcting codes (ECC) introduce redundancy into a sequence so that the receiver can correct errors that may occur during transmission over a noisy channel. The implementation of the modulation constraint, however, can often interfere with the error-correcting code. For hard-decision ECCs, such as Reed-Solomon codes, it turns out that a modified concatenation scheme, in which the positions of the modulation code and the ECC are reversed, can reduce error-propagation.; Error-correcting codes with soft iterative decoding algorithms, such as turbo codes and low-density parity check (LDPC) codes, have shown extremely good performance, approaching theoretical limits. The decoding algorithms for these codes are considered using the framework of factor graphs and the message-passing algorithm. Then turbo codes and LDPC codes are compared for the magnetic recording channel.; Finally, the modified concatenation scheme is applied to the problem of soft decoding, allowing the ECC decoder to obtain accurate soft information from the channel decoder. The interaction between the constrained code and the ECC is of fundamental importance for the application of turbo and LDPC codes to digital recording systems that use a modulation constraint. In addition, it is possible to introduce a constraint decoder that updates the probabilities based on the knowledge of the modulation constraint. Iterating between the constraint decoder and the ECC decoder can yield additional coding gain beyond the gain of the ECC.