Low-Density Parity-Check (LDPC) codes are the best error-correcting codes known for a wide variety of communications applications. The AR4JA code family encompasses encoders and decoders for nine error-correcting codes. These include Accumulate, Repeat-by-4, and Jagged Accumulate (AR4JA) codes developed at JPL.

An LDPC code and its encoder are described mathematically by a sparse parity check matrix and corresponding generator matrix. The encoding and decoding algorithms may be implemented in either software or hardware, with the preferred technology and programming language determined by data rate, compatibility with existing systems, ease of modification, and other factors. For each code, there are the following items: the parity check and generator matrices (in MATLAB format), three implementations of the encoder (Verilog hardware description language, and equivalent versions in C and MATLAB), and three implementations of the decoder (Verilog hardware description language, and equivalent versions in C and MATLAB). While not all items are immediately available for all nine codes, additional combinations can be implemented on demand without extensive work.

These implementations are designed specifically for the AR4JA code structures, and have been optimized for speed on the Xilinx Virtex-2 series of Field Programmable Gate Arrays (FPGAs). This speed is achieved by capitalizing on the protograph-plus-circulant construction of these codes.

This work was done by Kenneth S. Andrews, Dariush Divsalar, Samuel J. Dolinar, Jr., Christopher R. Jones, Fabrizio Pollara, and Jon Hamkins of Caltech; and Jeremy C. Thorpe of Google 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.. Refer to NPO-47162.


NASA Tech Briefs Magazine

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

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