Applications of iterative decoding to magnetic recording channels.

Finally, Q-ary LDPC (Q-LDPC) codes are considered for MRCs. Belief propagation decoding for binary LDPC codes is extended to Q-LDPC codes and a reduced-complexity decoding algorithm for Q-LDPC codes is developed. Q-LDPC coded systems perform very well with random noise as well as with burst erasures. Simulations show that Q-LDPC systems outperform RS systems.Secondly, binary low-density parity-check (LDPC) codes are proposed for MRCs. Random binary LDPC codes, finite-geometry LDPC codes and irregular LDPC codes are considered. With belief propagation decoding, LDPC systems are shown to have superior performance over current Reed-Solomon (RS) systems at the range possible for computer simulation. The issue of RS-LDPC concatenation is also addressed.Three coding schemes are investigated for magnetic recording systems. Firstly, block turbo codes, including product codes and parallel block turbo codes, are considered on MRCs. Product codes with other types of component codes are briefly discussed.Magnetic recoding channels (MRCs) are subject to noise contamination and error-correcting codes (ECCs) are used to keep the integrity of the data. Conventionally, hard decoding of the ECCs is performed. In this dissertation, systems using soft iterative decoding techniques are presented and their improved performance is established

Low Complexity Rate Compatible Puncturing Patterns Design for LDPC Codes

In contemporary digital communications design, two major challenges should be addressed: adaptability and flexibility. The system should be capable of flexible and efficient use of all available spectrums and should be adaptable to provide efficient support for the diverse set of service characteristics. These needs imply the necessity of limit-achieving and flexible channel coding techniques, to improve system reliability. Low Density Parity Check (LDPC) codes fit such requirements well, since they are capacity-achieving. Moreover, through puncturing, allowing the adaption of the coding rate to different channel conditions with a single encoder/decoder pair, adaptability and flexibility can be obtained at a low computational cost.In this paper, the design of rate-compatible puncturing patterns for LDPCs is addressed. We use a previously defined formal analysis of a class of punctured LDPC codes through their equivalent parity check matrices. We address a new design criterion for the puncturing patterns using a simplified analysis of the decoding belief propagation algorithm, i.e., considering a Gaussian approximation for message densities under density evolution, and a simple algorithmic method, recently defined by the Authors, to estimate the threshold for regular and irregular LDPC codes on memoryless binary-input continuous-output Additive White Gaussian Noise (AWGN) channels

Coded Slotted ALOHA: A Graph-Based Method for Uncoordinated Multiple Access

In this paper, a random access scheme is introduced which relies on the combination of packet erasure correcting codes and successive interference cancellation (SIC). The scheme is named coded slotted ALOHA. A bipartite graph representation of the SIC process, resembling iterative decoding of generalized low-density parity-check codes over the erasure channel, is exploited to optimize the selection probabilities of the component erasure correcting codes via density evolution analysis. The capacity (in packets per slot) of the scheme is then analyzed in the context of the collision channel without feedback. Moreover, a capacity bound is developed and component code distributions tightly approaching the bound are derived.Comment: The final version to appear in IEEE Trans. Inf. Theory. 18 pages, 10 figure