Turbo Product Codes for Optical Communications

With the increasing demand for high-speed communications systems, forward error correction (FEC) codes and signal processing techniques receive much attention. FEC is a mathematical method for introducing redundancy in a data stream or data block to protect information symbols against potential errors during transmission through a communications channel. A major breakthrough in FEC was achieved in 1993 with the introduction of iterative decoding of parallel concatenated recursive systematic convolutional codes, i.e., turbo codes. Turbo codes can achieve near-optimum performance levels at low signal to noise ratios, and have been successfully applied to wireless links, and also to deep-space and satellite communications. Another class of turbo-like codes is turbo product codes (TPC). In contrast to the “original” convolutional turbo codes, TPC’s are based on block codes and have significantly less decoding complexity and storage requirements. Therefore, TPC’s are more suitable for high data transmission rates such as those anticipated in optical networks. In this talk, we first review the TPC decoding concept and present a very low-complexity decoding algorithm for TPC’s that consist of extended Hamming component codes. Since no approximations are used, our proposed algorithm has absolutely no performance degradation when compared to the original TPC decoding algorithm. Besides efficient TPC decoding, we also propose a new parallel decoding approach that halves decoding time while maintaining virtually the same performance level. After introducing fast TPC decoding methods, we show how these codes can be adapted for optical code division multiple access (CDMA) networks. Our simulation results reveal that a significant increase in number of users and/or reduction of bandwidth expansion is possible for optical CDMA. The second TPC application area we consider is performance improvement of multimode fiber (MMF) links that are widely deployed for local area networks. Using actual measured fiber impulse responses, we show that the combination of a spatially resolved equalizer and a TPC decoder enables enhancement of the bandwidth-distance product for MMF links.