Concatenated Polar and Non binary LDPC codes for High Reliability in Optical Communication System

Next-generation high-speed optical transport systems require powerful forward error correction (FEC) codes with high error-correcting capabilities to ensure high data reliability. Low density parity check (LDPC) codes are strong candidates for ensuring the high data reliability needed to support data rates of 100 Gb/s, demanded by optical systems. Non-binary LDPC (NB-LDPC) codes provides better performance compared to binary version, as they offer larger coding gains with shorter code lengths and reduced system latency. Despite their advantages, LDPC codes suffer from error floor problem at low bit error rates (BER), with NB-LDPC codes showing error floors at BER around 10<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-7</sup>. High-speed optical transport systems generally require BERs of the order of 10<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-12</sup>. The error floor problem can be mitigated by concatenating LDPC codes with a shorter outer code. Existing works mainly focus on employing Reed Solomon (RS) codes to remove error floor. However, the decoding complexity is high for these codes. This paper proposes concatenated Polar and NB-LDPC codes to address the error floor issue, since polar codes have relatively low encoding and decoding complexity. The channel noise in optical communication systems using optical amplifiers cannot be analyzed using simplified additive white Gaussian noise (AWGN). Hence the channel noise is mathematically derived and proved that chi-square channel model is appropriate than AWGN. Simulation results demonstrate that the proposed concatenated codes over proposed channel model can achieve a net coding gain of around 1.5dB at a BER of 10<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-12</sup>.