New Combinatorial Construction Techniques for Low-Density Parity-Check Codes and Systematic Repeat-Accumulate Codes

• Published in: IEEE transactions on communications Vol. 60; no. 9; pp. 2387 - 2395
• Main Authors: Gruner, A., Huber, M.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.09.2012; Institute of Electrical and Electronics Engineers
• Subjects: accumulator design; Applied sciences; Coding, codes; combinatorial design; Decoding; Encoding; Exact sciences and technology; Information, signal and communications theory; Low-density parity-check (LDPC) code; Optical telecommunications; Orbits; Parity check codes; Signal and communications theory; Sparse matrices; Sum product algorithm; systematic repeat-accumulate (RA) code; Systematics; Systems, networks and services of telecommunications; Telecommunications; Telecommunications and information theory; Transmission and modulation (techniques and equipments); Performance evaluation; sum-product algorithm; Low-density parity-check (LDPC) code; accumulator design; Optical telecommunication; Repeat-accumulate code; Transmission channel; Decoding; Algorithm; systematic repeat-accumulate (RA) code; Combinatorial method; Error correcting code; Parity check codes; combinatorial design; Parity check; Magnetic recording
• ISSN: 0090-6778; 1558-0857
• DOI: 10.1109/TCOMM.2012.070912.110164

This paper presents several new construction techniques for low-density parity-check (LDPC) and systematic repeat-accumulate (RA) codes. Based on specific classes of combinatorial designs, the improved code design focuses on high-rate structured codes with constant column weights 3 and higher. The proposed codes are efficiently encodable and exhibit good structural properties. Experimental results on decoding performance with the sum-product algorithm show that the novel codes offer substantial practical application potential, for instance, in high-speed applications in magnetic recording and optical communications channels.