A Study of Error Floor Behavior in QC-MDPC Codes

A Monte Carlo method for calculating strength functions in many-fermion systems

Best linear unbiased prediction when error vector is correlated with other random vectors in the model

We introduce randomized Limited View (LV) adversary codes that provide protection against an adversary that uses their partial view of the channel to construct an adversarial error vector that is added to the channel. For a codeword of length N, the adversary selects a subset of size <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ρr</sub> N of components to “see”, and then “adds” an adversarial error vector of weight <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ρw</sub> N to the codeword. Performance of the code is measured by the probability of the decoder failure in recovering the sent message. An (N, q <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">RN</sup> , δ)-limited view adversary is a code of rate R that ensures that the success chance of the adversary in making decoder to fail is bounded by δ. Our main motivation to study these codes is providing protection for wireless communication at the physical layer of networks. We formalize the definition of adversarial error and decoder failure, construct a code with efficient encoding and decoding that allows the adversary to, depending on the code rate, read up to half of the sent codeword and add error on the same coordinates. The code is non-linear, has an efficient decoding algorithm, and is constructed using a message authentication code (MAC) and a Folded Reed-Solomon (FRS) code. The decoding algorithm uses an innovative approach that combines the list decoding algorithm of the FRS codes and the MAC verification algorithm to eliminate the exponential size of the list output from the decoding algorithm. We discuss our results and future work.

Talagrand’s inductive method and isoperimetric inequalities involving random sets

Concordance measures for multivariate non-continuous random vectors

The effect of random errors in the steering vector of an Applebaum adaptive array is examined. Each component of the steering vector is assumed to have a random error component uncorrelated between elements. The array output signal-to-interferenceplus-noise ratio (SINR) is computed as a function of the error variance. It is shown that the array output SINR becomes more sensitive to steering vector errors as more elements are added to the array and as the received desired signal power becomes larger. The variance of the steering vector error that may be tolerated depends on the required desired signal dynamic range. The larger the dynamic range that must be accommodated, the smaller the error variance must be.

A study of linear time-varying systems subject to stochastic disturbances

Distributed Luby transform (DLT) codes achieve a significant performance improvement in multi-source relay networks compared with the individual Luby transform (LT) code designed for each source. Since the DLT codes preserve the properties of the LT codes, the error floor is dominated by the low variable-node degrees in the bipartite graph, developed for iterative message passing decoding. Therefore, we analyze the error floor of the DLT codes for a multi-source, single relay, and a single destination network over additive white Gaussian noise (AWGN) channels. We modify the encoding process at the sources and propose a new relay combining scheme at the relay. The encoding process at the sources and the combining scheme at the relay are coordinated with the aim of improving the error floor performance of the proposed DLT codes. We derive a lower bound of the bit error probability of the DLT codes over AWGN channels. Furthermore, we optimize the relay degree distribution in terms of the overhead by using the framework of extrinsic information transfer chart analysis. The numerical results confirm that the proposed DLT coding scheme significantly outperforms the conventional scheme, especially in the error floor region.

Forward error-correcting (FEC) codes play an important role in transmitting data with extremely high reliability through modern communication systems. Many applications such as optical communication channels require a very low error rate when transmitting data. In this thesis, we study the design and analysis of low-density parity-check (LDPC) codes in general and spatially coupled (SC) LDPC codes in particular. At first, we analyze the error floor performance of finite-length protographbased spatially coupled LDPC codes in terms of their design parameters. We conduct a comprehensive analysis to show that the parameter syndrome former memory (m) plays the main role in the average number of cycles and trapping sets in the Tanner graph of finite-length SC-LDPC codes. This, in fact, gives an insight into the error floor performance of protograph-based SC-LDPC codes, and demonstrates the superiority of these codes in the error floor region, compared to their block code counterparts.

In this study, the authors introduce an efficient secure channel coding (joint cryptography-channel coding) scheme based on Latin square low-density lattice codes (Latin square LDLCs) over unconstrained power additive white Gaussian noise channel. They benefit the properties of Latin square LDLCs to dramatically reduce the key size of the proposed scheme while having an acceptable level of security compared with previous similar schemes. To reduce the key size, they consider two approaches: (i) saving the generating sequence of parity-check matrix of used Latin square LDLC as the part of secret key set; (ii) employing the Hermite normal form of the generator matrix of used Latin square LDLC as the encryption matrix. To provide an acceptable level of security, they consider three other strategies: (i) applying two hard problems related to lattices, i.e. shortest basis problem and closest vector problem; (ii) using a random rational vector as the perturbation (error) vector; (iii) exploiting the special joint encryption/LDLC encoding and joint decryption/LDLC decoding algorithms. Besides, the study discusses other efficiency analysis results consisting error performance and computational complexity of the proposed scheme.

SUMMARY This paper presents an improved version of multistage threshold decoding with a difference register (MTD-DR) for selforthogonal convolutional codes (SOCCs). An approximate lower bound on the bit error rate (BER) with the maximum likelihood (ML) decoding is also given. MTD-DR is shown to achieve an approximate lower bound of ML decoding performance at the higher Eb/N0. The code with larger minimum Hamming distance reduces the BER in error floor, but the BER in waterfall shifts to the higher Eb/N0. This paper gives a decoding scheme that improves the BER in both directions, waterfall and error floor. In the waterfall region, a 2-step decoding (2SD) improves the coding gain of 0.40 dB for shorter codes (code length 4200) and of 0.55 dB for longer codes (code length 80000) compared to the conventional MTD-DR. The 2-step decoding that serially concatenates the parity check (PC) decoding improves the BER in the error floor region. This paper gives an effective use of PC decoding, that further makes the BER 1/8 times compared to the ordinary use of PC decoding in the error floor region. Therefore, the 2SD with effective use of parity check decoding improves the BER in the waterfall and the error floor regions simultaneously.

Conditional upper bounds are given for min-sum decoding of low-density parity-check codes in the error floor region. It is generally thought that absorbing sets, i.e., small collections of variable nodes connected to a relatively small number of unsatisfied check nodes, are the primary source of errors in the error floor region. The conditional upper bounds presented here are based on the assumption that all error floor errors are caused by absorbing sets. In order to bound the probability of error associated with each absorbing set, a directed-edge Tanner graph is used to link absorbing sets to low-weight deviations. These low-weight deviations result when a proportionally large number of nodes within a stopping set belong to an absorbing set contained inside the stopping set. A complete collection of the most problematic absorbing sets, and the minimum deviation weights that result from them, are used to derive a conditional upper bound on the probability of error for min-sum decoding of low-density parity-check codes. Simulation results are given to demonstrate the accuracy of the bound.

Low-density parity check (LDPC) codes with their near-Shannon capacity limit error correcting performance and iterative decoding algorithm are being evaluated for digital communications applications. For LDPC codes to be used in real systems, their error floors need to be investigated. In this paper, we evaluate the performance of disjoint difference set (DDS)-based LDPC codes (with column weights 3, 4, 5) and array code-based LDPC codes (with column weights 3, 4, 5) in the additive white Gaussian noise (AWGN) channel using a high-speed field programmable gate array (FPGA) simulation platform. The error floor regions (bit error rates down to 10/sup -12/) of those codes are presented. For better performance of array codes, a girth optimization method is proposed and the FPGA evaluation results are presented.

본 논문은 오류 마루 영역에서 우수한 성능을 가지는 비이진 LDPC (low-density parity-check) 부호의 설계 방법을 제안하고 성능을 검증한다. 제안된 설계 방법은 비이진 LDPC 부호의 이진 최소 거리(binary minimum distance)를 최대화하도록 패리티 검사 행렬의 비이진 원소 값들을 결정한다. BPSK (binary phase-shift keying) 변조 방식 하에서 제안된 방법으로 설계된 비이진 LDPC 부호가 오류 마루(error floor) 영역에서 우수한 성능을 가지는 것을 Monte Carlo 시뮬레이션과 중요도 표본 추출(importance sampling) 기법을 사용하여 검증한다. In this paper we propose a design algorithm for nonbinary LDPC (low-density parity-check) codes with low error-floors. The proposed algorithm determines the nonbinary values of the nonzero entries in the parity-check matrix in order to maximize the binary minimum distance of the designed nonbinary LDPC codes. We verify the performance of the designed nonbinary LDPC codes in the error-floor region by Monte Carlo simulation and importance sampling over BPSK (binary phase-shift keying) modulation.

In modern taxi networks, large amounts of taxi occupancy status and location data are collected from networked in-vehicle sensors in real- time. They provide knowledge of system models on passenger demand and mobility patterns for efficient taxi dispatch and coordination strategies. Such approaches face a new challenge: how to deal with uncertainties of predicted customer demand while fulfilling the system's performance requirements, including minimizing taxis' total idle mileage and maintaining service fairness across the whole city. To address this problem, we develop a data- driven robust taxi dispatch framework to consider spatial-temporally correlated demand uncertainties. The robust optimization problem has an objective function that is concave in the uncertain demand and convex in the decision variables, and constraints that are convex in the decision variables according to the practical requirements. We design a data-driven algorithm for constructing uncertainty sets of random demand vectors that provide a probabilistic guarantee for the performance of robust taxi dispatch solutions. It guarantees that the probability that the actual dispatch cost under the true demand vector being smaller than the optimal cost of the robust dispatch solutions with the uncertainty sets is greater than a desired probability value. We prove equivalent computationally tractable forms of the robust dispatch problem with the constructed closed convex polytope and second order cone types of uncertainty sets, using the minimax theorem and strong duality. Evaluations on four years of taxi trip data for New York City show that the probabilistic guarantee is satisfied. By selecting a probabilistic guarantee level that does not sacrifice the average cost much, the average demand- supply ratio error is reduced by 31.7%, and the average total idle driving distance is reduced by 10.13% compared with non-robust dispatch solutions.