Iterative algebraic forward error-correction schemes for optical high-speed networks

• Applicant: Dr.-Ing. Christian Senger
• Subject Area: Electronic Semiconductors, Components and Circuits, Integrated Systems, Sensor Technology, Theoretical Electrical Engineering
• Term: from 2012 to 2015
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 226704771

Optical high-speed networks require bit error rates (BER) below 10^-15. Such small BER can be achieved by using forward-error-correcting codes. For fixed code rate, the channel coding theorem by Shannon allows to calculate the limiting channel error probability that allows to transmit with arbitrarilysmall BER. There exist iterative decoders for certain codes, whose BER approach this so-called Shannon limit. However, these iterative Decoders induce an exuberant data flow that is not manageable cost-efficiently for transmission rates of 100 Gigabit/s or more. Such transmission rates are common in optical high-speed networks. In the framework of this research project, iterative application of algebraic decoding shall be investigated. Generally, its data flow is significantly smaller than that of the classical iterative approaches mentioned above. Algebraic codes are a well-investigated field in coding theory and highlyefficient decoders are known. Smith et al. showed in a recent paper that they can be used as a building block for staircase codes. The authors provided an iterative decoding algorithm and showed that the achievable BER approaches the Shannon limit as the theoretical optimum.Previous results on staircase codes are based on rather classical assumptions, e.g., none of thebest currently known algebraic decoding algorithms are applied. Their application has far-reaching influence on the decoding of staircase codes, but it has some obvious potentials due to the structural code properties and the error patterns that occur during the iterative decoding process. It shall beinvestigated how recent results of the applicant and other authors can be used in order to significantly improve the decoding of staircase codes, which gains are possible in doing so, and which impact does the improvement have on practical implementations.A main focus of the project shall be on the utilization of reliability information, meaningthat the decoder is provided with the probability whether a received bit is correct or not. It is well-known that this allows for a considerable reduction of the BER of non-iterative algebraic decoders. On that account, it is promising to find a non-trivial extension of the iterative decoding algorithmfor staircase codes. In this context, active branches of coding theory like soft-decision list decoding with the Koetter-Vardy algorithm, collaborative decoding of block codes, and adaptive Chase-decoding will be accessed.

• DFG Programme: Research Fellowships
• International Connection: Canada
• Host: Professor Frank R. Kschischang, Ph.D.