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

TL;DR

This paper introduces new combinatorial construction methods for LDPC and systematic RA codes, focusing on high-rate, efficiently encodable codes with good structural properties, suitable for high-speed communication applications.

Contribution

The paper proposes novel combinatorial design-based construction techniques for LDPC and RA codes, enhancing code structure and decoding performance.

Findings

Codes exhibit high decoding performance with sum-product algorithm

Constructed codes are efficiently encodable and structurally robust

Potential applications in magnetic recording and optical communications

Abstract

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.