Accumulate-Repeat-Accumulate-Accumulate Codes

NASA’s Jet Propulsion Laboratory, Pasadena, California

Saturday, September 01 2007 Other rate-1/2 ARAA examples with maximum variable node degree 4 (but with larger protographs) can reduce the threshold further. ARAA codes with higher code rates can be obtained by puncturing the output of the middle accumulator: For example, one can obtain thresholds of 1.46 dB and 2.00 dB for rates 2/3 and 3/4, respectively, for punctured versions of the ARAA code represented in the bottom part of the figure. A single fast decoder using a belief-propagation algorithm with depuncturing can be implemented to handle different code rates.

By use of density evolution (a computational-simulation technique for analyzing performances of LDPC codes) on protographs of ARAA codes of maximum variable node degree 4, it has been found that a minimum bit signal-to-noise ratio as low as 0.21 dB above the channel capacity limit can be achieved as the block size goes to infinity. Such a low threshold cannot be achieved by RA, irregular RA (IRA), or unstructured irregular LDPC codes with the same constraint on the maximum variable node degree. Furthermore, by puncturing the accumulators, one can construct families of higher rate ARAA codes with thresholds that stay close to their respective channel capacity thresholds. Results of simulations of iterative decoding have shown that ARAA codes would perform comparably to the best previously known LDPC codes but with very low error floors, even at moderate block sizes.

This work was done by Dariush Divsalar, Samuel Dolinar, and Jeremy Thorpe of Caltech for NASA’s Jet Propulsion Laboratory.

In accordance with Public Law 96-517, the contractor has elected to retain title to this invention. Inquiries concerning rights for its commercial use should be addressed to:
Innovative Technology Assets Management
JPL
Mail Stop 202-233
4800 Oak Grove Drive
Pasadena, CA 91109-8099
(818) 354-2240
E-mail: This e-mail address is being protected from spambots. You need JavaScript enabled to view it

Refer to NPO-41305, volume and number of this NASA Tech Briefs issue, and the page number.