Minimum-Variance Importance-Sampling Bernoulli Estimator for Fast Simulation of Linear Block Codes over Binary Symmetric Channels

In this paper the choice of the Bernoulli distribution as biased distribution for importance sampling (IS) Monte-Carlo (MC) simulation of linear block codes over binary symmetric channels (BSCs) is studied. Based on the analytical derivation of the optimal IS Bernoulli distribution, with explicit calculation of the variance of the corresponding IS estimator, two novel algorithms for fast-simulation of linear block codes are proposed. For sufficiently high signal-to-noise ratios (SNRs) one of the proposed algorithm is SNR-invariant, i.e. the IS estimator does not depend on the cross-over probability of the channel. Also, the proposed algorithms are shown to be suitable for the estimation of the error-correcting capability of the code and the decoder. Finally, the effectiveness of the algorithms is confirmed through simulation results in comparison to standard Monte Carlo method

Error-Floors of the 802.3an LDPC Code for Noise Assisted Decoding

In digital communication, information is sent as bits, which is corrupted by the noise present in wired/wireless medium known as the channel. The Low Density Parity Check (LDPC) codes are a family of error correction codes used in communication systems to detect and correct erroneous data at the receiver. Data is encoded with error correction coding at the transmitter and decoded at the receiver. The Noisy Gradient Descent BitFlip (NGDBF) decoding algorithm is a new algorithm with excellent decoding performance with relatively low implementation requirements. This dissertation aims to characterize the performance of the NGDBF algorithm. A simple improvement over NGDBF called the Re-decoded NGDBF (R-NGDBF) is proposed to enhance the performance of NGDBF decoding algorithm. A general method to estimate the decoding parameters of NGDBF is presented. The estimated parameters are then verified in a hardware implementation of the decoder to validate the accuracy of the estimation technique

Importance Sampling for Coded-Modulation Error Probability Estimation

This paper proposes an efficient simulation method based on importance sampling to estimate the random-coding error probability of coded modulation. The technique is valid for complex-valued modulations over Gaussian channels, channels with memory, and naturally extends to fading channels. The simulation method is built on two nested importance samplers to respectively estimate the pairwise error probability and generate the channel input and output. The effect of the respective number of samples on the overall bias and variance of the estimate of the error probability is characterized. For a memoryless channel, the estimator is shown to be consistent and with a small variance, growing with the square root of the code length, rather than the exponential growth of a standard Monte Carlo estimator.This work has been funded in part by the European Research Council under ERC grant agreement 725411, and by the Spanish Ministry of Economy and Competitiveness under grant TEC2016-78434-C3-1-R

Synchronization for capacity -approaching coded communication systems

The dissertation concentrates on synchronization of capacity approaching error-correction codes that are deployed in noisy channels with very low signal-to-noise ratio (SNR). The major topics are symbol timing synchronization and frame synchronization.;Capacity-approaching error-correction codes, like turbo codes and low-density parity-check (LDPC) codes, are capable of reaching very low bit error rates and frame error rates in noisy channels by iterative decoding. To fully achieve the potential decoding capability of Turbo codes and LDPC codes, proper symbol timing synchronization, frame synchronization and channel state estimation are required. The dissertation proposes a joint estimator of symbol time delay and channel SNR for symbol timing recovery, and a maximum a posteriori (MAP) frame synchronizer for frame synchronization.;Symbol timing recovery is implemented by sampling and interpolation. The received signal is sampled multiple times per symbol period with unknown delay and unknown SNR. A joint estimator estimates the time delay and the SNR. The signal is rebuilt by interpolating available samples using estimated time delay. The intermediate decoding results enable decision-feedback estimation. The estimates of time delay and SNR are refined by iterative processing. This refinement improves the system performance significantly.;Usually the sampling rate is assumed to be a strict integer multiple of the symbol rate. However, in a practical system the local oscillators in the transmitter and the receiver may have random drifts. Therefore the sampling rate is no longer an exact multiple of the symbol rate, and the sampling time follows a random walk. This random walk may harm the system performance severely. The dissertation analyzes the effect of random time walks and proposes to mitigate the effect by overlapped sliding windows and iterative processing.;Frame synchronization is required to find the correct boundaries of codewords. MAP frame synchronization in the sense of minimizing the frame sync failure rate is investigated. The MAP frame synchronizer explores low-density parity-check attributes of the capacity-approaching codes. The accuracy of frame synchronization is adequate for considered coded systems to work reliably under very low SNR

Raptor Codes for BIAWGN Channel: SNR Mismatch and the Optimality of the Inner and Outer Rates

Fountain codes are a class of rateless codes with two interesting properties, first, they can generate potentially limitless numbers of encoded symbols given a finite set of source symbols, and second, the source symbols can be recovered from any subset of encoded symbols with cardinality greater than the number of source symbols. Raptor codes are the first implementation of fountain codes with linear complexity and vanishing error floors on noisy channels. Raptor codes are designed by the serial concatenation of an inner Luby trans-form (LT) code, the first practical realization of fountain codes, and an outer low-density parity-check (LDPC) code. Raptor codes were designed to operate on the binary erasure channel (BEC), however, since their invention they received considerable attention in or-der to improve their performance on noisy channels, and especially additive white Gaussiannoise (AWGN) channels. This dissertation considers two issues that face Raptor codes on the binary input additive white Gaussian noise (BIAWGN) channel: inaccurate estimation of signal to noise ratio (SNR) and the optimality of inner and outer rates. First, for codes that use a belief propagation algorithm (BPA) in decoding, such as Raptor codes on the BIAWGN channel, accurate estimation of the channel SNR is crucial to achieving optimal performance by the decoder. A difference between the estimated SNR and the actual channel SNR is known as signal to noise ratio mismatch (SNRM). Using asymptomatic analysis and simulation, we show the degrading effects of SNRM on Raptor codes and observe that if the mismatch is large enough, it can cause the decoding to fail. Using the discretized density evolution (DDE) algorithm with the modifications required to simulate the asymptotic performance in the case of SNRM, we determine the decoding threshold of Raptor codes for different values of SNRM ratio. Determining the threshold under SNRM enables us to quantify its effects which in turn can be used to reach important conclusions about the effects of SNRM on Raptor codes. Also, it can be used to compare Raptor codes with different designs in terms of their tolerance to SNRM. Based on the threshold response to SNRM, we observe that SNR underestimation is slightly less detrimental to Raptor codes than SNR overestimation for lower levels of mismatch ratio, however, as the mismatch increases, underestimation becomes more detrimental. Further, it can help estimate the tolerance of a Raptor code, with certain code parameters when transmitted at some SNR value, to SNRM. Or equivalently, help estimate the SNR needed for a given code to achieve a certain level of tolerance to SNRM. Using our observations about the performance of Raptor codes under SNRM, we propose an optimization method to design output degree distributions of the LT part that can be used to construct Raptor codes with more tolerance to high levels of SNRM. Second, we study the effects of choosing different values of inner and outer code rate pairs on the decoding threshold and performance of Raptor codes on the BIAWGN channel. For concatenated codes such as Raptor codes, given any instance of the overall code rate R, different inner (Ri) and outer (Ro) code rate combinations can be used to share the available redundancy as long asR=RiRo. Determining the optimal inner and outer rate pair can improve the threshold and performance of Raptor codes. Using asymptotic analysis, we show the effect of the rate pair choice on the threshold of Raptor codes on the BIAWGN channel and how the optimal rate pair is decided. We also show that Raptor codes with different output degree distributions can have different optimal rate pairs, therefore, by identifying the optimal rate pair we can further improve the performance and avoid suboptimal use of the code. We make the observation that as the outer rate of Raptor codes increases the potential of achieving better threshold increases, and provide the reason why the optimal outer rate of Raptor codes cannot occur at lower values. Finally, we present an optimization method that considers the optimality of the inner and outer rates in designing the output degree distribution of the inner LT part of Raptor codes. The designed distributions show improvement in both the decoding threshold and performance compared to other code designs that do not consider the optimality of the inner and outer rates