The JPEG image compression standard is very sensitive to errors. Even though it contains error resilience features, it cannot easily cope with induced errors from computer soft faults prevalent in remote-sensing applications. Hence, new fault tolerance detection methods are developed to sense the soft errors in major parts of the system while also protecting data across the boundaries where data flow from one subsystem to the other. The design goal is to guarantee no compressed or decompressed data contain computer-induced errors without detection. Detection methods are expressed at the algorithm level so that a wide range of hardware and software implementation techniques can be covered by the fault tolerance procedures while still maintaining the JPEG output format. The major subsystems to be addressed are the discrete cosine transform, quantizer, entropy coding, and packet assembly. Each error detection method is determined by the data representations within the subsystem or across the boundaries. They vary from real number parities in the DCT to bit-level residue codes in the quantizer, cyclic redundancy check parities for entropy coding, and packet assembly. The simulation results verify detection performances even across boundaries while also examining roundoff noise effects in detecting computer-induced errors in processing steps.

Detecting computer-induced errors in remote-sensing JPEG compression algorithms

Wavelet transforms, central to multiresolution signal analysis and important in the JPEG2000 image compression standard, are quite susceptible to computer-induced errors because of their pipelined structure and multirate processing requirements. Such errors emanate from computer hardware, software bugs, or radiation effects from the surrounding environment. Implementations use lifting schemes, which employ update and prediction estimation stages, and can spread a single numerical error caused by failures to many output transform coefficients without any features to warn data users. We propose an efficient method to detect the arithmetic errors using weighted sums of the wavelet coefficients at the output compared with an equivalent parity value derived from the input data. Two parity values may straddle a complete multistage transform or several values may be used, each pair covering a single stage. There is greater error-detecting capability at only a slight increase in complexity when parity pairs are interspersed between stages. With the parity weighting design scheme, a single error introduced at a lifting section can be detected. The parity computation operation is properly viewed as an inner product between weighting values and the data, motivating the use of dual space functionals related to the error gain matrices. The parity weighting values are generated by a combination of dual space functionals. An iterative procedure for evaluating the design of the parity weights has been incorporated in Matlab code and simulation results are presented.

Concurrent error detection in wavelet lifting transforms

Inspired by photonic one-way quantum computation, we describe a microwave signal processing method for implementing unitary transforms based on measuring the cebits encoded in the “classical microwave graph state (CMGS).” Here the terms “cebit” and “CMGS” defined in our system are classical analogies of a qubit and certain target quantum graph states in quantum physics respectively, which can exhibit some similar behaviors and resultants. The constructions of 4- and 16-cebit CMGSs as examples are discussed in detail and specific tomography methods are introduced to characterize their qualities. By performing operations on these CMGSs, we implement some basic 2 × 2, 4 × 4, and specific generalized unitary transforms, and obtain output results with high fidelities. Furthermore, we also demonstrate that a simulation of an efficient Grover’s search algorithm, which has been executed in one-way quantum computing schemes, can be directly realized via a certain 4-cebit CMGS. Due to the excellent parallel efficiency and credible outcomes in the proposal, this quantum-inspired method may provide benefits for exploring new ways to microwave information processing, or in turn as an alternative tool for simulating particular quantum systems to some extent.

Quantum-inspired microwave signal processing for implementing unitary transforms.

A novel concurrent soft error detection and correction scheme is introduced for parallel hardware implementations of transform-based convolution. The proposed technique is based on the structure of radix-2 Fast Fourier Transforms (FFT) of length 2n where n is an integer. The scheme can provide up to 100 percent detection and correction of isolated single soft errors in the convolution at the cost of little more than double the system area, rather than triple, as is required when using conventional Triple Modular Redundancy (TMR).

Offset DMR: A Low Overhead Soft Error Detection and Correction Technique for Transform-Based Convolution

In this paper, we propose a generic weighted checksum code based quality aware error detection scheme for 2-D separable linear transformation. These key components are widely used in multimedia compression systems, e.g., video and image codecs. The technique encodes the input array at the 2-D linear transformation level, and algorithms are designed to operate on encoded data and produce encoded output data. The proposed error detection technique is a system-level method therefore can be used in existing hardware or software 2-D linear transformation architectures with low overhead. More importantly, the proposed weighted checksum code based error detection can enable quality metric aware error detection which only flags an error when the quality of the result is lower than expectation. The error tolerance detection technique can fit perfectly in multimedia compression systems.

Quality Aware Error Detection in 2-D Separable Linear Transformation

Discrete fast unitary transform algorithms, of which the fast Fourier transform (FFT) and fast discrete Cosine transform (DCT) are practical examples, are highly susceptible to temporary calculation failures because of their interconnected computational flows. Many error detection techniques for FFT algorithms have been reported, but fault tolerance issues for other important transforms have not been addressed as vigorously. A general design and analysis approach for all fast unitary transforms is presented. It relies on fundamental linear algebra methods coupled with associated dual space representations that are natural descriptions of real parity values. Basic output error patterns from single computational errors are used to define an equal-sized group of dual space basis vectors on which practical parity weighting functions may be evaluated. An iterative design approach leads to complete single error detection capabilities. FFT and fast DCT examples are given.

G.R. Redinbo

Papers

Concurrent error detection in fast unitary transform algorithms