arXiv subjects

Yunghsiang S. Han

Publications and source records attributed to Yunghsiang S. Han.

46 records · Page 3Linked to original sources

arXiv2014

Maximum-likelihood Soft-decision Decoding for Binary Linear Block Codes Based on Their Supercodes

Based on the notion of supercodes, we propose a two-phase maximum-likelihood soft-decision decoding (tpMLSD) algorithm for binary linear block codes in this work. The first phase applies the Viterbi algorithm backwardly to a trellis derived from the parity-check matrix of the supercode of the linear block code. Using the information retained from the first phase, the second phase employs the priority-first search algorithm to the trellis corresponding to the linear block code itself, which guarantees finding the ML decision. Simulations on Reed-Muller codes show that the proposed two-phase scheme is an order of magnitude more efficient in average decoding complexity than the recursive maximum-likelihood decoding (RMLD) [1] when the signal-to-noise ratio per information bit is 4.5 dB.

cs.IT↗

arXiv2014

Novel Polynomial Basis and Its Application to Reed-Solomon Erasure Codes

In this paper, we present a new basis of polynomial over finite fields of characteristic two and then apply it to the encoding/decoding of Reed-Solomon erasure codes. The proposed polynomial basis allows that $h$-point polynomial evaluation can be computed in $O(h\log_2(h))$ finite field operations with small leading constant. As compared with the canonical polynomial basis, the proposed basis improves the arithmetic complexity of addition, multiplication, and the determination of polynomial degree from $O(h\log_2(h)\log_2\log_2(h))$ to $O(h\log_2(h))$. Based on this basis, we then develop the encoding and erasure decoding algorithms for the $(n=2^r,k)$ Reed-Solomon codes. Thanks to the efficiency of transform based on the polynomial basis, the encoding can be completed in $O(n\log_2(k))$ finite field operations, and the erasure decoding in $O(n\log_2(n))$ finite field operations. To the best of our knowledge, this is the first approach supporting Reed-Solomon erasure codes over characteristic-2 finite fields while achieving a complexity of $O(n\log_2(n))$, in both additive and multiplicative complexities. As the complexity leading factor is small, the algorithms are advantageous in practical applications.

cs.IT↗

arXiv2014

Distributed Inference with M-ary Quantized Data in the Presence of Byzantine Attacks

The problem of distributed inference with M-ary quantized data at the sensors is investigated in the presence of Byzantine attacks. We assume that the attacker does not have knowledge about either the true state of the phenomenon of interest, or the quantization thresholds used at the sensors. Therefore, the Byzantine nodes attack the inference network by modifying modifying the symbol corresponding to the quantized data to one of the other M symbols in the quantization alphabet-set and transmitting the false symbol to the fusion center (FC). In this paper, we find the optimal Byzantine attack that blinds any distributed inference network. As the quantization alphabet size increases, a tremendous improvement in the security performance of the distributed inference network is observed. We also investigate the problem of distributed inference in the presence of resource-constrained Byzantine attacks. In particular, we focus our attention on two problems: distributed detection and distributed estimation, when the Byzantine attacker employs a highly-symmetric attack. For both the problems, we find the optimal attack strategies employed by the attacker to maximally degrade the performance of the inference network. A reputation-based scheme for identifying malicious nodes is also presented as the network's strategy to mitigate the impact of Byzantine threats on the inference performance of the distributed sensor network.

cs.IT↗

arXiv2013

Target Localization in Wireless Sensor Networks using Error Correcting Codes

In this work, we consider the task of target localization using quantized data in Wireless Sensor Networks (WSNs). We propose an energy efficient localization scheme by modeling it as an iterative classification problem. We design coding based iterative approaches for target localization where at every iteration, the Fusion Center (FC) solves an M-ary hypothesis testing problem and decides the Region of Interest (ROI) for the next iteration. The coding based iterative approach works well even in the presence of Byzantine (malicious) sensors in the network. We further consider the effect of non-ideal channels. We suggest the use of soft-decision decoding to compensate for the loss due to the presence of fading channels between the local sensors and the FC. We evaluate the performance of the proposed schemes in terms of the Byzantine fault tolerance capability and probability of detection of the target region. We also present performance bounds which help us in designing the system. We provide asymptotic analysis of the proposed schemes and show that the schemes achieve perfect region detection irrespective of the noise variance when the number of sensors tends to infinity. Our numerical results show that the proposed schemes provide a similar performance in terms of Mean Square Error (MSE) as compared to the traditional Maximum Likelihood Estimation (MLE) but are computationally much more efficient and are resilient to errors due to Byzantines and non-ideal channels.

stat.AP↗

arXiv2013

Distributed Detection in Tree Topologies with Byzantines

In this paper, we consider the problem of distributed detection in tree topologies in the presence of Byzantines. The expression for minimum attacking power required by the Byzantines to blind the fusion center (FC) is obtained. More specifically, we show that when more than a certain fraction of individual node decisions are falsified, the decision fusion scheme becomes completely incapable. We obtain closed form expressions for the optimal attacking strategies that minimize the detection error exponent at the FC. We also look at the possible counter-measures from the FC's perspective to protect the network from these Byzantines. We formulate the robust topology design problem as a bi-level program and provide an efficient algorithm to solve it. We also provide some numerical results to gain insights into the solution.

stat.AP↗

arXiv2013

Update-Efficient Regenerating Codes with Minimum Per-Node Storage

Regenerating codes provide an efficient way to recover data at failed nodes in distributed storage systems. It has been shown that regenerating codes can be designed to minimize the per-node storage (called MSR) or minimize the communication overhead for regeneration (called MBR). In this work, we propose a new encoding scheme for [n,d] error- correcting MSR codes that generalizes our earlier work on error-correcting regenerating codes. We show that by choosing a suitable diagonal matrix, any generator matrix of the [n,α] Reed-Solomon (RS) code can be integrated into the encoding matrix. Hence, MSR codes with the least update complexity can be found. An efficient decoding scheme is also proposed that utilizes the [n,α] RS code to perform data reconstruction. The proposed decoding scheme has better error correction capability and incurs the least number of node accesses when errors are present.

cs.IT↗

arXiv2011

Exact Regenerating Codes for Byzantine Fault Tolerance in Distributed Storage

Due to the use of commodity software and hardware, crash-stop and Byzantine failures are likely to be more prevalent in today's large-scale distributed storage systems. Regenerating codes have been shown to be a more efficient way to disperse information across multiple nodes and recover crash-stop failures in the literature. In this paper, we present the design of regeneration codes in conjunction with integrity check that allows exact regeneration of failed nodes and data reconstruction in presence of Byzantine failures. A progressive decoding mechanism is incorporated in both procedures to leverage computation performed thus far. The fault-tolerance and security properties of the schemes are also analyzed.

cs.IT↗

arXiv2007

Maximum-Likelihood Priority-First Search Decodable Codes for Combined Channel Estimation and Error Protection

The code that combines channel estimation and error protection has received general attention recently, and has been considered a promising methodology to compensate multi-path fading effect. It has been shown by simulations that such code design can considerably improve the system performance over the conventional design with separate channel estimation and error protection modules under the same code rate. Nevertheless, the major obstacle that prevents from the practice of the codes is that the existing codes are mostly searched by computers, and hence exhibit no good structure for efficient decoding. Hence, the time-consuming exhaustive search becomes the only decoding choice, and the decoding complexity increases dramatically with the codeword length. In this paper, by optimizing the signal-tonoise ratio, we found a systematic construction for the codes for combined channel estimation and error protection, and confirmed its equivalence in performance to the computer-searched codes by simulations. Moreover, the structural codes that we construct by rules can now be maximum-likelihoodly decodable in terms of a newly derived recursive metric for use of the priority-first search decoding algorithm. Thus,the decoding complexity reduces significantly when compared with that of the exhaustive decoder. The extension code design for fast-fading channels is also presented. Simulations conclude that our constructed extension code is robust in performance even if the coherent period is shorter than the codeword length.

cs.IT↗

arXiv2007

Analysis of Sequential Decoding Complexity Using the Berry-Esseen Inequality

his study presents a novel technique to estimate the computational complexity of sequential decoding using the Berry-Esseen theorem. Unlike the theoretical bounds determined by the conventional central limit theorem argument, which often holds only for sufficiently large codeword length, the new bound obtained from the Berry-Esseen theorem is valid for any blocklength. The accuracy of the new bound is then examined for two sequential decoding algorithms, an ordering-free variant of the generalized Dijkstra's algorithm (GDA)(or simplified GDA) and the maximum-likelihood sequential decoding algorithm (MLSDA). Empirically investigating codes of small blocklength reveals that the theoretical upper bound for the simplified GDA almost matches the simulation results as the signal-to-noise ratio (SNR) per information bit ($γ_b$) is greater than or equal to 8 dB. However, the theoretical bound may become markedly higher than the simulated average complexity when $γ_b$ is small. For the MLSDA, the theoretical upper bound is quite close to the simulation results for both high SNR ($γ_b\geq 6$ dB) and low SNR ($γ_b\leq 2$ dB). Even for moderate SNR, the simulation results and the theoretical bound differ by at most \makeblue{0.8} on a $\log_{10}$ scale.

cs.IT↗

arXiv2007

Analysis of the Sufficient Path Elimination Window for the Maximum-Likelihood Sequential-Search Decoding Algorithm for Binary Convolutional Codes

A common problem on sequential-type decoding is that at the signal-to-noise ratio (SNR) below the one corresponding to the cutoff rate, the average decoding complexity per information bit and the required stack size grow rapidly with the information length. In order to alleviate the problem in the maximum-likelihood sequential decoding algorithm (MLSDA), we propose to directly eliminate the top path whose end node is $Δ$-trellis-level prior to the farthest one among all nodes that have been expanded thus far by the sequential search. Following random coding argument, we analyze the early-elimination window $Δ$ that results in negligible performance degradation for the MLSDA. Our analytical results indicate that the required early elimination window for negligible performance degradation is just twice of the constraint length for rate one-half convolutional codes. For rate one-third convolutional codes, the required early-elimination window even reduces to the constraint length. The suggestive theoretical level thresholds almost coincide with the simulation results. As a consequence of the small early-elimination window required for near maximum-likelihood performance, the MLSDA with early-elimination modification rules out considerable computational burdens, as well as memory requirement, by directly eliminating a big number of the top paths, which makes the MLSDA with early elimination very suitable for applications that dictate a low-complexity software implementation with near maximum-likelihood performance.

cs.IT↗