The decoding performance of polar codes strongly depends on the decoding algorithm used, while also the decoder throughput and its latency mainly depend on the decoding algorithm. In this work, we implement the powerful successive cancellation list (SCL) decoder on a GPU and identify the bottlenecks of this algorithm with respect to parallel computing and its difficulties. The inherent serial decoding property of the SCL algorithm naturally limits the achievable speed-up gains on GPUs when compared to CPU implementations. In order to increase the decoding throughput, we use a hybrid decoding scheme based on the belief propagation (BP) decoder, which can be intraand inter-frame parallelized. The proposed scheme combines excellent decoding performance and high throughput within the signal-to-noise ratio (SNR) region of interest.
In this paper, data-transmission using the nonlinear Fourier transform for jointly modulated discrete and continuous spectra is investigated. A recent method for purely discrete eigenvalue removal at the detector is extended to signals with additional continuous spectral support. At first, the eigenvalues are sequentially detected and removed from the jointly modulated received signal. After each successful removal, the time-support of the resulting signal for the next iteration can be narrowed, until all eigenvalues are removed. The resulting truncated signal, ideally containing only continuous spectral components, is then recovered by a standard NFT algorithm. Numerical simulations without a fiber channel show that, for jointly modulated discrete and continuous spectra, the mean-squared error between transmitted and received eigenvalues can be reduced using the eigenvalue removal approach, when compared to state-of-the-art detection methods. Additionally, the computational complexity for detection of both spectral components can be decreased when, by the choice of the modulated eigenvalues, the time-support after each removal step can be reduced. Numerical simulations are also carried out for transmission over a Raman-amplified, lossy SSMF channel. The mutual information is approximated and the eigenvalue removal method is shown to result in achievable rate improvements.
With the seemingly inevitable "capacity crunch" for state-of-the-art fiber optical systems, alternatives to wavelength-division-multiplexing are widely discussed in the community. Recently, modulation schemes based on the nonlinear Fourier transform have been proposed, where the transmit signal is generated by modulating both the continuous and discrete nonlinear spectrum. This full spectrum nonlinear Fourier transform algorithm and its inverse are investigated and existing methods are extended to modulation of the entire nonlinear spectrum.
Expectation maximization clustering of received nonlinear spectral data from solitonic pulses is used to reduce bit error rates. Simulations over a 1800 km Raman amplified fiber link demonstrate the effectiveness of the method.
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