A Refined Scaling Law for Spatially Coupled LDPC Codes Over the Binary Erasure Channel

We propose a refined scaling law to predict the finite-length performance in the waterfall region of spatially coupled low-density parity-check codes over the binary erasure channel. In particular, we introduce some improvements to the scaling law proposed by Olmos and Urbanke that result in a better agreement between the predicted and simulated frame error rate. We also show how the scaling law can be extended to predict the bit error rate performance.Comment: Paper accepted to IEEE Information Theory Workshop (ITW) 201

Finite-Length Scaling Laws for Spatially-Coupled LDPC Codes

This thesis concerns predicting the finite-length error-correcting performance of spatially-coupled low-density parity-check (SC-LDPC) code ensembles over the binary erasure channel. SC-LDPC codes are a very powerful class of codes; their use in practical communication systems, however, requires the system designer to specify a considerable number of code and decoder parameters, all of which affect both the code’s error-correcting capability and the system’s memory, energy, and latency requirements. Navigating the space of the associated trade-offs is challenging. The aim of the finite-length scaling laws proposed in this thesis is to facilitate code and decoder parameter optimization by providing a way to predict the code’s error-rate performance without resorting to Monte-Carlo simulations for each combination of code/decoder and channel parameters.First, we tackle the problem of predicting the frame, bit, and block error rate of SC-LDPC code ensembles over the binary erasure channel under both belief propagation (BP) decoding and sliding window decoding when the maximum number of decoding iterations is unlimited. The scaling laws we develop provide very accurate predictions of the error rates.Second, we derive a scaling law to accurately predict the bit and block error rate of SC-LDPC code ensembles with doping, a technique relevant for streaming applications for limiting the inherent rate loss of SC-LDPC codes. We then use the derived scaling law for code parameter optimization and show that doping can offer a way to achieve better transmission rates for the same target bit error rate than is possible without doping.Last, we address the most challenging (and most practically relevant) case where the maximum number of decoding iterations is limited, both for BP and sliding window decoding. The resulting predictions are again very accurate.Together, these contributions make finite-length SC-LDPC code and decoder parameter optimization via finite-length scaling laws feasible for the design of practical communication systems

Photochemical Initiation of Polariton Propagation

Placing a material inside an optical cavity can enhance transport of excitation energy by hybridizing excitons with confined light modes into polaritons, which have a dispersion that provides these light-matter quasi-particles with low effective masses and very high group velocities. While in experiments polariton propagation is typically initiated with laser pulses, tuned to be resonant either with the polaritonic branches that are delocalized over many molecules, or with an uncoupled higher-energy electronic excited state that is localized on a single molecule, practical implementations of polariton-mediated exciton transport into devices would require operation under low-intensity incoherent light conditions. Here, we propose to initiate polaritonic exciton transport with a photo-acid, which upon absorption of a photon in a spectral range not strongly reflected by the cavity mirrors, undergoes ultra-fast excited-state proton transfer into a red-shifted excited-state photo-product that can couple collectively with a large number of suitable dye molecules to the modes of the cavity. By means of atomistic molecular dynamics simulations we demonstrate that cascading energy from a photo-excited donor into the strongly coupled acceptor-cavity states can indeed induce long-range polariton-mediated exciton transport

Tuning the Coherent Propagation of Organic Exciton-Polaritons through the Cavity Q-factor

Transport of excitons in organic materials can be enhanced through polariton formation when the interaction strength between these excitons and the confined light modes of an optical resonator exceeds their decay rates. While the polariton lifetime is determined by the Q(uality)-factor of the optical resonator, the polariton group velocity is not. Instead, the latter is solely determined by the polariton dispersion. Yet, experiments suggest that the Q-factor also controls the polariton propagation velocity. To understand this observation, we performed molecular dynamics simulations of Rhodamine chromophores strongly coupled to Fabry-P\'erot cavities with various Q-factors. Our results suggest that propagation in the aforementioned experiments is initially dominated by ballistic motion of upper polariton states at their group velocities, which leads to a rapid expansion of the wavepacket. Cavity decay in combination with non-adiabatic population transfer into dark states, rapidly depletes these bright states, causing the wavepacket to contract. However, because population transfer is reversible, propagation continues, but as a diffusion process, at lower velocity. By controlling the lifetime of bright states, the Q-factor determines the duration of the ballistic phase and the diffusion coefficient in the diffusive regime. Thus, polariton propagation in organic microcavities can be effectively tuned through the Q-factor.Comment: arXiv admin note: text overlap with arXiv:2209.0730

Secondary emission of nanocrystalline zinc oxide

The Raman and photoluminescence (PL) spectra of nanocrystalline zinc oxide produced by mechanochemical synthesis were measured using a pulsed nitrogen laser (337.1 nm) and xenon lamp (360 nm) as excitation sources in PL measurements and a cw Nd:YAG laser in Raman measurements. PL was observed in the range 400&ndash;800 nm. The Raman spectrum of nanocrystalline (90 nm) ZnO was compared to that of coarsegrained ZnO. The Raman bands of nanocrystalline zinc oxide were found to be shifted to lower frequencies and broadened. Laser radiation was shown to cause local heating of zinc oxide up to 1000 K, resulting in photoinduced formation of zinc nanoclusters. Mixtures of zinc oxide and sodium chloride powders are heated to substantially lower temperatures. Under nitrogen laser excitation, the green PL band (535 nm), characteristic of bulk ZnO, is shifted to longer wavelengths by 85 nm. The results are interpreted in terms of light confinement in zinc oxide microclusters consisting of large number of nanocrystallites. The photoinduced processes in question may be a viable approach to producing metal-insulator structures in globular photonic crystals, opals, filled with zinc oxide.<br /

Finite-Length Scaling of Spatially Coupled LDPC Codes Under Window Decoding Over the BEC

We analyze the finite-length performance of spatially coupled low-density parity-check (SC-LDPC) codes under window decoding over the binary erasure channel. In particular, we propose a refinement of the scaling law by Olmos and Urbanke for the frame error rate (FER) of terminated SC-LDPC ensembles under full belief propagation (BP) decoding. The refined scaling law models the decoding process as two independent Ornstein-Uhlenbeck processes, in correspondence to the two decoding waves that propagate toward the center of the coupled chain for terminated SC-LDPC codes. We then extend the proposed scaling law to predict the performance of (terminated) SC-LDPC code ensembles under the more practical sliding window decoding. Finally, we extend this framework to predict the bit error rate (BER) and block error rate (BLER) of SC-LDPC code ensembles. The proposed scaling law yields very accurate predictions of the FER, BLER, and BER for both full BP and window decoding.Comment: Published in IEEE Transactions on Communications (Early Access). This paper was presented in part at the IEEE Information Theory Workshop (ITW), Visby, Sweden, August 2019 (arXiv:1904.10410