G. Van Meerbergen

A Hierarchical Symmetric Stereo Algorithm Using Dynamic Programming

In this paper, a new hierarchical stereo algorithm is presented. The algorithm matches individual pixels in corresponding scanlines by minimizing a cost function. Several cost functions are compared. The algorithm achieves a tremendous gain in speed and memory requirements by implementing it hierarchically. The images are downsampled an optimal number of times and the disparity map of a lower level is used as ‘offset’ disparity map at a higher level. An important contribution consists of the complexity analysis of the algorithm. It is shown that this complexity is independent of the disparityrange. This result is also used to determine the optimal number of downsample levels. This speed gain results in the ability to use more complex (compute intensive) cost functions that deliver high quality disparity maps. Another advantage of this algorithm is that cost functions can be chosen independent of the optimisation algorithm. The algorithm in this paper is symmetric, i.e. exactly the same matches are found if left and right image are swapped. Finally, the algorithm was carefully implemented so that a minimal amount of memory is used. It has proven its efficiency on large images with a high disparity range as well as its quality. Examples are given in this paper.

Reed-solomon codes implementing a coded single-carrier with cyclic prefix scheme

This paper presents a novel Reed-Solomon codes based transmission scheme called RS-SC-CP. While RS-SC-CP is essentially a Reed-Solomon (RS) coded single carrier with cyclic prefix (SC-CP) system, a filter bank representation of the RS code is used. This filter bank representation unveils a DFT synthesis bank, just as in a traditional Orthogonal Frequency Division Multiplexing (OFDM) system (allbeit in a finite field). Therefore, RS-SC-CP is topologically equivalent with OFDM. As such, the RS-SC-CP system inherits the advantages of an SC-CP system over a traditional OFDM system like a low Peak to Average Power Ratio (PAPR). But, more importantly, it allows us to use a novel equalization technique that resembles a traditional OFDM equalizer. The equalizer of an RS-SC-CP receiver is split into two stages: the first stage encompasses a partial equalization in the complex field, which ensures that the residual channel response has integer coefficients. It is calculated using a Minimum Mean Square Error (MMSE) criterion. The residual ISI is removed by a Galois field equalizer in the second stage, posterior to the RS decoding removing the noise. Finally, the performance of the RS-SC-CP system is further evaluated by simulations showing the performance gain of the RS-SC-CP system compared to a traditional coded OFDM or single carrier with cyclic prefix (SC-CP) scheme.

Combining Reed-Solomon Codes and OFDM for Impulse Noise Mitigation: RS-OFDM

In this paper, a joint solution to the design problem of a good error-correcting code for an OFDM scheme with a low peak to average power ratio (PAPR) in the case of impulse noise is presented. The PAPR problem is tackled by decomposing the circulant channel matrix into parallel channels by using DFT matrices in a Galois field of odd characteristic, rather than in a complex field. The modulo operation inherent to this field then limits the power of the modulated signal. More importantly, it is explained how this OFDM scheme can be seamlessly merged with a Reed-Solomon (RS) code, which due to its maximal Hamming distance is the preferred code for impulse noise cancellation. The overall scheme, referred to as RS-OFDM, shows an error correcting code that is matched to the OFDM-modulator. It is shown that the optimal Hamming distance of the RS code is preserved not only by the OFDM modulator, but also by the channel

Critically Subsampled Filterbanks for SISO Reed–Solomon Decoding

In the last decade, there has been a growing interest in soft decoding techniques. These techniques are used in the context of concatenated codes, with Turbo codes as the main example, but are almost never applied to existing classical codes. In this paper, the family of Reed-Solomon (RS) codes is considered, and the complexity problem of soft-in soft-out (SISO) RS decoding is tackled by breaking RS codes into several smaller subcodes. Finally, the decoders of these subcodes work together in a Turbo-like fashion (Gallagers algorithm) to find an approximate maximum a posteriori (MAP) solution. The decomposition that is presented here is based on critically subsampled filterbanks, with one subcode in each subband. A critically subsampled filterbank allows us to define a number of parallel independent subcodes. Furthermore, noncritically subsampled filterbanks have a larger number of subband variables than the codeword length, causing a message passing decoder (Gallagers algorithm) to fail. This paper focuses on the construction of such filterbanks, starting from noncritically subsampled filterbanks, it gradually evolves towards a critically subsampled filterbank

Critically subsampled filterbanks implementing Reed-Solomon codes

The last decade has shown a growing interest in soft decoding techniques. These techniques are almost never applied to existing nearly perfect codes, but instead other families of concatenated codes arise with Turbo codes as the main example. The problem is that for the application of soft decoding, the perfect codes need to be broken into several smaller component codes. In this paper, the family of Reed-Solomon codes is considered, and, using filterbanks, they are broken into several component codes (one in each subband). This paper focuses on the construction of such filterbanks, and gradually evolves towards a critically subsampled filterbank. The critical subsampling is crucial if the filterbank is going to be used in a soft decoding setup.

Turbo-like soft-decision decoding of Reed-Solomon codes

We aim to bridge the gap between classical coding theory and soft decoding. Reed-Solomon (RS) codes are chosen as an example, and a few standard possibilities for a soft RS decoder are explored. Soon, it is noticed that the resulting (standard) algorithms are too complex and/or not very performant. However, by employing a special critically sampled filter bank representation for the RS codes, an algorithm is developed that shows a good tradeoff between computational complexity and soft decoding performance. Furthermore, it is demonstrated that this algorithm shows remarkable similarities with turbo codes, thereby preserving the perfectness of the original RS code.

Filterbank Decompositions for (Non)-Systematic Reed–Solomon Codes With Applications to Soft Decoding

This paper focuses on Reed-Solomon (RS) codes, which are the most widespread classical error correcting codes. Recently, we have shown that an finite-impulse response (FIR) critically subsampled filterbank representation can be derived for some RS codes. However, this work only addresses RS codes with a non-coprime codeword and dataword length, seriously limiting its practical usability. In this paper, an alternative purely algebraic method is presented to construct such a filterbank. Apart from providing additional insight into the algebraic structure of (non-systematic) RS codes, this method is suited to eliminate the non-coprimeness constraint mentioned before. Using this filterbank decomposition, a RS code is broken into smaller subcodes that can subsequently be used to build a soft-in soft-out (SISO) RS decoder. It is shown how any RS code, written as an FIR filterbank, can be SISO decoded using the filterbank based decoder. Owing to the importance of systematic RS codes, it is shown that any systematic RS code can be decoded using the FIR filterbank decomposition. This leads to better decoding performance in addition with a slightly lower complexity. A further extension towards systematic RS codes is also presented in this paper resulting in an infinite-impulse response critically subsampled filterbank representation.

Soft-in soft-out Reed-Solomon decoding using critically subsampled filterbanks

In the last decade, there has been a growing interest in soft decoding techniques. These techniques are used in the context of concatenated codes, with Turbo codes as the main example, but are almost never applied to existing classical codes. In this paper, the family of Reed-Solomon codes is considered and the complexity problem of Soft-In Soft-Out RS decoding is tackled by breaking RS codes into several smaller subcodes. The decomposition, presented here, is based on filterbanks with one subcode in each subband. The critical subsampling is then crucial if the filterbank is going to be used in a soft decoding setup. This paper focuses on the construction of such filterbanks, starting from non-critically subsampled filterbanks and evolving to a critically subsampled filterbank.

Using AsteRxi GNSS/MEMS IMU receiver in a container positioning system

High-end GNSS receivers are deployed in rapidly increasing numbers in industrial applications. Their challenging operational environment exposes the vulnerability of GNSS technology. For example, container terminal operators in harbors are increasingly using GNSS positioning for their container positioning systems. The primary goal of using GNSS in such an application is to reduce the amount of lost containers for economical and safety reasons. Therefore, it is important to track each container in a reliable and accurate manner. While this is typically not an issue for the positioning of containers on the yard for professional GNSS receivers due to open-sky conditions, problems arise below cranes and in the vicinity of ship hulls. At these locations, a GNSS-only position solution is insufficient due to the large metal surfaces which cause low measurement availability and increase the possibility that signals are tracked via indirect paths.

Filterbank decompositions for BCH-codes with applications to soft decoding and code division multiple acces systems

Multirate systems and filterbanks are known to be powerful tools in image and audio applications. Recently, they are also recognised to play an important role in communication systems. This paper covers the use of filterbanks in a coding context. It is shown that their inherent periodically time varying character matches remarkably well with the cyclic properties of the family of Bose-Chaudhuri-Hochquenghem (BCH) codes. In this paper, the important subclass of Reed-Solomon (RS) codes is dealt with first. This section of the paper proves that an RS code can be implemented by a critically subsampled filterbank. The redundancy is added by the subbandfilters, which are shown to be variants of non-primitive BCH codes. The second part of the paper deals with BCH codes. In this part, a BCH code is decomposed as a sum of critically subsampled filterbanks. The critical subsampling is an important aspect in a number of applications. The use of these filterbanks in a CDMA system and in a soft-in soft-out (SISO) decoding context is briefly discussed