Hung-Ta Pai

On eigenstructure-based direct multichannel blind image restoration

Existing eigenstructure-based direct multichannel blind image restoration techniques include nullspace-based and direct deconvolver estimation techniques. The nullspace-based approach can be formulated as an optimization problem. We show that this formulation implies a new subspace-based approach that uses matrix operations. This new approach has the same advantages as the nullspace-based one but requires less computational complexity. Under some mild conditions, its complexity is equal to that of the FFT. Furthermore, the relation among the nullspace-based approach, the direct deconvolver estimation and the new subspace-based approach is studied.

Low-complexity ML decoding for convolutional tail-biting codes

Recently, a maximum-likelihood (ML) decoding algorithm with two phases has been proposed for convolutional tailbiting codes. The first phase applies the Viterbi algorithm to obtain the trellis information, and then the second phase employs the algorithm A* to find the ML solution. In this work, we improve the complexity of the algorithm A* by using a new evaluation function. Simulations showed that the improved A* algorithm has over 5 times less average decoding complexity in the second phase when Eb/N0ges 4 dB.

Exact multichannel blind image restoration

Liu and Xu (see ibid., vol.43, no.11, p.2714-23, 1995) proposed a blind symbol estimation algorithm in digital communications. If all the channels are linear time-invariant finite impulse response (LTI FIR) filters, this algorithm can estimate symbols exactly when the channels and the input symbols satisfy some loose restrictions. We extend this algorithm to two dimensions, and in particular, to multichannel (noise-free) blind image restoration. Assuming linear FIR blur functions, given at least three blurred versions of the same image, and loose restrictions (different from those of Liu and Xu) on the original image and on the blur functions, the original image can be exactly recovered, up to a scalar multiplier.

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.

Efficient Exact Regenerating Codes for Byzantine Fault Tolerance in Distributed Networked Storage

Todays large-scale distributed storage systems are commonly built using commodity software and hardware. As a result, crash-stop and Byzantine failures in such systems become more and more prevalent. In the literature, regenerating codes have been shown to be a more efficient way to disperse information across multiple storage nodes and recover from crash-stop failures. In this paper, we propose a novel decoding design of product-matrix constructed regenerating codes in conjunction with integrity check that allows exact regeneration of failed nodes and data reconstruction in the presence of Byzantine failures. A progressive decoding mechanism is incorporated in both procedures to leverage computation performed thus far. Unlike previous works, our new regenerating code decoding has the advantage that its building blocks, such as Reed-Solomon codes and standard cryptographic hash functions, are relatively well-understood because of their widespread applications. The fault tolerance and security properties of the proposed schemes are also analyzed. In addition, the performance of the proposed schemes, in terms of the average number of access nodes and the reconstruction failure probability versus the node failure probability, are also evaluated by Monte Carlo simulations.

New HARQ Scheme Based on Decoding of Tail-Biting Convolutional Codes in IEEE 802.16e

Traditionally, a hybrid automatic repeat request (HARQ) is executed at the physical (PHY) and medium access control (MAC) layers. A cyclic redundancy check (CRC) is usually performed at the MAC layer to decide whether a packet must be retransmitted. This design causes two problems-long latency and inefficient retransmission-when a transmission error appears in a large packet. In this paper, we propose a new HARQ scheme to solve these problems based not only on CRC but on the decoding of tail-biting convolutional codes (TBCCs) at the PHY layer as well. First, the TBCC codeword that was received at the decoder is cyclically shifted according to the reliability of the received code bits. The Viterbi algorithm (VA), starting from all states, is then applied. When every survival path in the VA is close enough to its corresponding abandoned path, retransmission of the codeword is invoked. Because retransmission is restricted to a codeword and determined at the PHY layer, short latency and efficient retransmission are achieved. Simulation results show that the proposed scheme reduces the number of retransmitted codewords by up to 43% compared with the traditional HARQ in IEEE 802.16e orthogonal frequency-division multiple access (OFDMA) under a Rayleigh faded channel when the 1024-point fast Fourier transform (FFT) and 64-state quadrature amplitude modulation (64-QAM) are employed.

Two-dimensional coded classification schemes in wireless sensor networks

This work proposes a novel fault-tolerant classification system based on distributed detection and two-dimensional channel coding. A rule is then derived to reduce the search space such that the optimal code matrix can be found. Simulation results reveal that the proposed scheme has higher classification reliability and better capability of fault tolerance than previous methods. Moreover, a code matrix using repetition codes is presented. The proposed scheme with the repetition code has a lower memory requirement at each sensor and higher detection flexibility than that with the optimal code matrix while only having a slightly lower performance. Finally, an asymptotic performance analysis is provided for the proposed scheme.

Adaptive Retransmission for Distributed Detection in Wireless Sensor Networks

An approach combining distributed detection with error-correcting codes has recently been proposed to design a fault-tolerant classification system in wireless sensor networks. The detection result of each sensor must be transmitted to a fusion center for making a final decision. The mis-classification probability using this approach is high when the transmission channel is highly noisy. This work proposes a novel adaptive retransmission algorithm to improve the mis classification probability. The fusion center calculates reliability of each received detection result while making the final decision. When the final decision is not reliable, the sensor which has sent the received result with the lowest reliability will be asked to retransmit its detection result by the fusion center. Simulation results show that the misclassification probability can be effectively reduced through the retransmission

Reliability-Based Adaptive Distributed Classification in Wireless Sensor Networks

In many wireless sensor networks, local sensors adopt binary decisions because they can be transmitted to a fusion center using very low power. However, if a binary decision is wrong, the probability of the fusion center making a wrong final decision is dramatically increased. This study proposes a reliability-based adaptive method to resolve this problem with little extra computation. Before a sensor makes a binary local decision, its observation must be evaluated. Unreliable ranges are set for this evaluation. If the sensors observation result does not fall within the unreliable range, the sensor makes a local decision. Otherwise, the sensor must make another observation. The optimal unreliable ranges are then derived. This study applies the proposed method to an existing distributed classification scheme using the binary decision. Performance analysis shows that this approach efficiently reduces the misclassification probability at the fusion center. Simulation results show that the transmission power is reduced by 7.5 dB to achieve a misclassification probability of 0.1 under some practical conditions.

Update-Efficient Error-Correcting Product-Matrix Codes

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 new encoding schemes for error-correcting MSR and MBR codes that generalize our earlier results on error-correcting regenerating codes. General encoding schemes for product-matrix MSR and MBR codes are derived such that the encoder based on Reed-Solomon (RS) codes is no longer limited to the Vandermonde matrix proposed earlier. Furthermore, MSR codes and MBR codes with the least update complexity can be found. A decoding scheme is proposed that utilizes RS codes to perform data reconstruction for MSR codes. The proposed decoding scheme has better error correction capability and incurs least number of node accesses when errors are present. A new decoding scheme is also proposed for MBR codes that is more capable and can correct more error-patterns. Simulation results are presented that exhibit the superior performance of the proposed schemes.