Low-Density Parity Check Codes

Abstract

For high density magnetic recording channels and memory systems, low-density parity-check (LDPC) codes with probabilistic decoding are replacing Reed-Solomon (RS) codes or Bose-Chaudhuri-Hocquenghem (BCH) codes with conventional algebraic decoding. The main benefit of LDPC codes over the RS and BCH codes is that LDPC codes can provide lower error probabilities than equivalent conventional codes if the conditions of magnetic recording channels or memory systems are the same. In other words, in order to achieve the same error probabilities, LDPC codes can tolerate lower signal-to-noise-ratio conditions than the conventional codes, which can imply higher densities and lower media costs. These advantages of LDPC codes are possible at the cost of the increased decoder complexity over the conventional decoding.The main themes of this thesis are (1) to determine probabilistic input to the LDPC decoders from the channel detectors in magnetic recording channels or memory systems with low complexity and (2) AcknowledgmentsI would like to thank Prof. Kumar for providing me with a unique opportunity and an ideal environment to study signal processing and error correcting codes for data storage and memory systems. I respect his patience and believing in students. I was very lucky and I will miss the time I stayed here.I would like to thank Prof. Bain, Prof. Li, and Dr. Cheng for reading my thesis during their busiest time and providing many suggestions and very detailed feedback.I would also like to thank Dr. Cheng for bringing my interest into the fascinating problem of protecting memory systems on spacecraft and for his very detailed comments on the manuscripts of the papers on this topic.