A Low-Complexity RS-SPC Product Coding Scheme for Optical Systems

This paper presents a product coding scheme based on binary images of Reed-Solomon (RS) codes and single-parity-check (SPC) codes for high-speed communications. Utilizing the special selection of components, we propose hybrid soft- and hard-decision iterative decoding (ID) algorithms for these codes, during which many RS component decoders can be early terminated. The proposed hybrid ID only exchanges ternary messages between component decoders and early stops the RS component decoders satisfying a proposed stopping criterion, thus low hardware and computational complexities are guaranteed. The hybrid ID of RS-SPC product codes not only performs comparable to the soft-decision decoding of low-density parity-check (LDPC) codes and block turbo codes (BTCs), but also takes much lower computational complexity and smaller decoder data flow. We also propose semi-analytical methods to estimate the waterfall and error-floor performances of the proposed scheme, which yield relatively accurate estimated results. The simulation results and error-floor estimations indicate that some good RS-SPC product codes have very low error floors that satisfy the requirements of optical systems.