Coding and Decoding in High Photon Information Efficiency Systems

This article introduces a novel method to encode and decode large codeblocks across an optical channel operating in the high photon information efficiency (HPIE) regime using high-order pulse position modulation (PPM). Our approach relies on modular coding with a sparse matrix of circularly overlapping modular blocks. The decoding is tailored to the mix of high erasures associated with high PPM in HPIE, and occasional errors. The erasures are handled by Gauss-Jordan elimination, and the errors by using guesswork on PPM substitution errors. We compare the performance complexity of our scheme with Berlekamp Massey decoding of Reed Solomon codes, which constitute the state-of-the-art in HPIE with PPM. Our encoding/decoding approach achieves the same block error rate while reducing the number of operations needed to decode by orders of magnitude compared to the Berlekamp Massey decoding. The gains grow as the efficiency of the channel, which leads to higher order of the PPM, increases. Hence, our approach offers a scalable and flexible solution to the HPIE channels.