Writing (recording) to a storage device and reading from it can be considered as a noisy channel. A storage device such as magnetic recoding and optical recording can be modeled as a partial response channel. Partial-response techniques are a special case of precoding technique where the intersymbol interference is forced to some known pattern. Thus, read-back data from storage devices may have intersymbol interference.

Coding techniques are required for improving the reliability of data over such noisy partial response channels. Protograph codes have shown excellent performance over AWGN (Additive White Gaussian Noise) channels. However, a new class of protograph codes is needed because experiments show that a capacity approaching protograph code in the AWGN channel may not perform well in partial response channels. In particular, protographs with punctured nodes are often used to produce good AWGN codes, but they perform poorly with the BCJR equalizer.

Protograph-based LDPC (low-density parity-check) codes were designed for magnetic recording since they can be modeled as partial response channels. Other types of partial response channels are Intersymbol Interference (ISI) channels that happen in band-limited channels, and frequency selective multipath fading channels. The design method and construction of protograph-based LDPC codes here applies to magnetic recording and many other applications. A protograph-based LDPC code that can approach the independent and uniformly distributed (i.u.d.) capacity of partial response channels was developed. A method was proposed to calculate the iterative decoding threshold of a joint graph between a protograph and the state structure of a partial response channel using the extrinsic information transfer (EXIT) chart. A simple method was determined to search for a protograph code with threshold close to i.u.d. capacity.

The threshold was computed over the joint graph between the LDPC decoder and trellis nodes, which represent finite state partial response channels. At the receiver, two cases were discussed: (1) iteratively decode the big graph, namely BCJR-full; (2) only iterative LDPC graphs after taking outputs from the BCJR equalizer, namely BCJR-once. Decoding thresholds were computed, and the code performance was simulated for both cases. The focus was on graphs that possess good protograph properties having a low decoding threshold and the linear minimum distance growth property that guarantees no error floor if random circulants are assigned when lifting the protograph. Such graphs should have degree-1 variable nodes, a fraction of high degree nodes, and degree-2 nodes.

This work was done by Dariush Divsalar of Caltech, and Thuy V. Nguyen and Aria Nosratinia of the University of Dallas for NASA’s Jet Propulsion Laboratory. For more information, contact This email address is being protected from spambots. You need JavaScript enabled to view it.. This software is available for commercial licensing. Please contact Dan Broderick at This email address is being protected from spambots. You need JavaScript enabled to view it.. NPO-48408

NASA Tech Briefs Magazine

This article first appeared in the October, 2015 issue of NASA Tech Briefs Magazine.

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