Iterative algebraic forward error-correction schemes for optical high-speed networks
Final Report Abstract
Staircase codes are a promising code construction for application in optical high-speed networks. They consist of multiple, simple, but elaborately coupled, algebraic codes with fast decoders. The main outcome of this research project are improvements in the decoding algorithms for the most frequently used algebraic constituent codes of staircase codes, the RS and their subfield BCH subcodes. It has been shown that the Guruswami-Sudan list decoder, as the state of the art in RS decoding, can be simplified beyond the previously known re-encoding prefactors based on a simple property of the base field. In addition, under certain assumptions, the re-encoding projection can be performed in a near-trivial manner as a periodicity projection. As a result, we could show that Guruswami-Sudan list decoding can operate on much smaller mathematical objects (vectors, matrices, polynomials) than originally thought. This saves time and hardware complexity, which is crucial for application in staircase codes where a massive number of decoders must run simultaneously under (due to the high data rates in optical networks) tight data flow constraints. It has been shown that matrix displacement leads to a particularly hardware-friendly implementation of the Peterson algorithm, a classical method used to calculate an error locator polynomial from a syndrome. However, in the context of staircase codes, calculating error locator polynomials is only half the battle since, the errors also need to be located and evaluated. This is where interpolation-based decoding methods such at the CJuruswami-Sudan list decoding algorithm and its simpler variant for bounded minimum distance decoding, the Welch-Berlekamp algorithm, shine: they skip these steps altogether and calculate the transmitted message directly from the received vector. We have shown in the course of this project that both approaches can be combined, benefiting from the advantages of both of them.
Publications
- "On multi-trial Forney-Kovalev decoding of concatenated codes". Advances in Mathematics of Communications 8.1 (Feb. 2014). pp. 1-20
A. Chaaban, V. R. Sidorenko, and C. Senger
(See online at https://doi.org/10.3934/amc.2014.8.1) - "Prefactor reduction of the Guruswami-Sudan interpolation step". IEEE Trans. Inf. Theory 60.12 (Dec. 2014), pp. 1-13
C. Senger
(See online at https://doi.org/10.1109/TIT.2014.2361347) - "Re-encoding techniques for interpolation-based decoding of Reed-Solomon codes". 27th Queen's Biennial Symposium on Communications. 2014 (QBSC 2014). Kingston, ON, Canada, June 30, 2014, pp. 203-207
C. Senger
(See online at https://doi.org/10.1109/QBSC.2014.6841214) - "Sierpinski prefactors in the Guruswami-Sudan interpolation step". 2014 International Zurich Seminar on Communications, 2014 (IZS 2014). Zurich, Switzerland, Feb. 2014, pp. 83-86
C. Senger
(See online at https://doi.org/10.3929/ethz-a-010089041) - "A fast displacement-based Peterson decoder". 14th Canadian Workshop on Information Theory, 2015 (CWIT 2015). St. John's, NL, Canada: IEEE, July 2015, pp. 14-17
C. Senger and F. R. Kschischang
(See online at https://doi.org/10.1109/cwit.2015.7255142)
