Higher-order CIS codes

We introduce {\bf complementary information set codes} of higher-order. A binary linear code of length $tk$ and dimension $k$ is called a complementary information set code of order $t$ ($t$-CIS code for short) if it has $t$ pairwise disjoint information sets. The duals of such codes permit to reduce the cost of masking cryptographic algorithms against side-channel attacks. As in the case of codes for error correction, given the length and the dimension of a $t$-CIS code, we look for the highest possible minimum distance. In this paper, this new class of codes is investigated. The existence of good long CIS codes of order $3$ is derived by a counting argument. General constructions based on cyclic and quasi-cyclic codes and on the building up construction are given. A formula similar to a mass formula is given. A classification of 3-CIS codes of length $\le 12$ is given. Nonlinear codes better than linear codes are derived by taking binary images of $\Z_4$-codes. A general algorithm based on Edmonds' basis packing algorithm from matroid theory is developed with the following property: given a binary linear code of rate $1/t$ it either provides $t$ disjoint information sets or proves that the code is not $t$-CIS. Using this algorithm, all optimal or best known $[tk, k]$ codes where $t=3, 4, \dots, 256$ and $1 \le k \le \lfloor 256/t \rfloor$ are shown to be $t$-CIS for all such $k$ and $t$, except for $t=3$ with $k=44$ and $t=4$ with $k=37$.Comment: 13 pages; 1 figur

Bit rates in audio source coding

The goal is to introduce and solve the audio coding optimization problem. Psychoacoustic results such as masking and excitation pattern models are combined with results from rate distortion theory to formulate the audio coding optimization problem. The solution of the audio optimization problem is a masked error spectrum, prescribing how quantization noise must be distributed over the audio spectrum to obtain a minimal bit rate and an inaudible coding errors. This result cannot only be used to estimate performance bounds, but can also be directly applied in audio coding systems. Subband coding applications to magnetic recording and transmission are discussed in some detail. Performance bounds for this type of subband coding system are derived

Audio Coding Based on Integer Transforms

Die Audiocodierung hat sich in den letzten Jahren zu einem sehr populären Forschungs- und Anwendungsgebiet entwickelt. Insbesondere gehörangepasste Verfahren zur Audiocodierung, wie etwa MPEG-1 Layer-3 (MP3) oder MPEG-2 Advanced Audio Coding (AAC), werden häufig zur effizienten Speicherung und Übertragung von Audiosignalen verwendet. Für professionelle Anwendungen, wie etwa die Archivierung und Übertragung im Studiobereich, ist hingegen eher eine verlustlose Audiocodierung angebracht. Die bisherigen Ansätze für gehörangepasste und verlustlose Audiocodierung sind technisch völlig verschieden. Moderne gehörangepasste Audiocoder basieren meist auf Filterbänken, wie etwa der überlappenden orthogonalen Transformation "Modifizierte Diskrete Cosinus-Transformation" (MDCT). Verlustlose Audiocoder hingegen verwenden meist prädiktive Codierung zur Redundanzreduktion. Nur wenige Ansätze zur transformationsbasierten verlustlosen Audiocodierung wurden bisher versucht. Diese Arbeit präsentiert einen neuen Ansatz hierzu, der das Lifting-Schema auf die in der gehörangepassten Audiocodierung verwendeten überlappenden Transformationen anwendet. Dies ermöglicht eine invertierbare Integer-Approximation der ursprünglichen Transformation, z.B. die IntMDCT als Integer-Approximation der MDCT. Die selbe Technik kann auch für Filterbänke mit niedriger Systemverzögerung angewandt werden. Weiterhin ermöglichen ein neuer, mehrdimensionaler Lifting-Ansatz und eine Technik zur Spektralformung von Quantisierungsfehlern eine Verbesserung der Approximation der ursprünglichen Transformation. Basierend auf diesen neuen Integer-Transformationen werden in dieser Arbeit neue Verfahren zur Audiocodierung vorgestellt. Die Verfahren umfassen verlustlose Audiocodierung, eine skalierbare verlustlose Erweiterung eines gehörangepassten Audiocoders und einen integrierten Ansatz zur fein skalierbaren gehörangepassten und verlustlosen Audiocodierung. Schließlich wird mit Hilfe der Integer-Transformationen ein neuer Ansatz zur unhörbaren Einbettung von Daten mit hohen Datenraten in unkomprimierte Audiosignale vorgestellt.In recent years audio coding has become a very popular field for research and applications. Especially perceptual audio coding schemes, such as MPEG-1 Layer-3 (MP3) and MPEG-2 Advanced Audio Coding (AAC), are widely used for efficient storage and transmission of music signals. Nevertheless, for professional applications, such as archiving and transmission in studio environments, lossless audio coding schemes are considered more appropriate. Traditionally, the technical approaches used in perceptual and lossless audio coding have been separate worlds. In perceptual audio coding, the use of filter banks, such as the lapped orthogonal transform "Modified Discrete Cosine Transform" (MDCT), has been the approach of choice being used by many state of the art coding schemes. On the other hand, lossless audio coding schemes mostly employ predictive coding of waveforms to remove redundancy. Only few attempts have been made so far to use transform coding for the purpose of lossless audio coding. This work presents a new approach of applying the lifting scheme to lapped transforms used in perceptual audio coding. This allows for an invertible integer-to-integer approximation of the original transform, e.g. the IntMDCT as an integer approximation of the MDCT. The same technique can also be applied to low-delay filter banks. A generalized, multi-dimensional lifting approach and a noise-shaping technique are introduced, allowing to further optimize the accuracy of the approximation to the original transform. Based on these new integer transforms, this work presents new audio coding schemes and applications. The audio coding applications cover lossless audio coding, scalable lossless enhancement of a perceptual audio coder and fine-grain scalable perceptual and lossless audio coding. Finally an approach to data hiding with high data rates in uncompressed audio signals based on integer transforms is described

Audio Coding Based on Integer Transforms

Die Audiocodierung hat sich in den letzten Jahren zu einem sehr populären Forschungs- und Anwendungsgebiet entwickelt. Insbesondere gehörangepasste Verfahren zur Audiocodierung, wie etwa MPEG-1 Layer-3 (MP3) oder MPEG-2 Advanced Audio Coding (AAC), werden häufig zur effizienten Speicherung und Übertragung von Audiosignalen verwendet. Für professionelle Anwendungen, wie etwa die Archivierung und Übertragung im Studiobereich, ist hingegen eher eine verlustlose Audiocodierung angebracht. Die bisherigen Ansätze für gehörangepasste und verlustlose Audiocodierung sind technisch völlig verschieden. Moderne gehörangepasste Audiocoder basieren meist auf Filterbänken, wie etwa der überlappenden orthogonalen Transformation "Modifizierte Diskrete Cosinus-Transformation" (MDCT). Verlustlose Audiocoder hingegen verwenden meist prädiktive Codierung zur Redundanzreduktion. Nur wenige Ansätze zur transformationsbasierten verlustlosen Audiocodierung wurden bisher versucht. Diese Arbeit präsentiert einen neuen Ansatz hierzu, der das Lifting-Schema auf die in der gehörangepassten Audiocodierung verwendeten überlappenden Transformationen anwendet. Dies ermöglicht eine invertierbare Integer-Approximation der ursprünglichen Transformation, z.B. die IntMDCT als Integer-Approximation der MDCT. Die selbe Technik kann auch für Filterbänke mit niedriger Systemverzögerung angewandt werden. Weiterhin ermöglichen ein neuer, mehrdimensionaler Lifting-Ansatz und eine Technik zur Spektralformung von Quantisierungsfehlern eine Verbesserung der Approximation der ursprünglichen Transformation. Basierend auf diesen neuen Integer-Transformationen werden in dieser Arbeit neue Verfahren zur Audiocodierung vorgestellt. Die Verfahren umfassen verlustlose Audiocodierung, eine skalierbare verlustlose Erweiterung eines gehörangepassten Audiocoders und einen integrierten Ansatz zur fein skalierbaren gehörangepassten und verlustlosen Audiocodierung. Schließlich wird mit Hilfe der Integer-Transformationen ein neuer Ansatz zur unhörbaren Einbettung von Daten mit hohen Datenraten in unkomprimierte Audiosignale vorgestellt.In recent years audio coding has become a very popular field for research and applications. Especially perceptual audio coding schemes, such as MPEG-1 Layer-3 (MP3) and MPEG-2 Advanced Audio Coding (AAC), are widely used for efficient storage and transmission of music signals. Nevertheless, for professional applications, such as archiving and transmission in studio environments, lossless audio coding schemes are considered more appropriate. Traditionally, the technical approaches used in perceptual and lossless audio coding have been separate worlds. In perceptual audio coding, the use of filter banks, such as the lapped orthogonal transform "Modified Discrete Cosine Transform" (MDCT), has been the approach of choice being used by many state of the art coding schemes. On the other hand, lossless audio coding schemes mostly employ predictive coding of waveforms to remove redundancy. Only few attempts have been made so far to use transform coding for the purpose of lossless audio coding. This work presents a new approach of applying the lifting scheme to lapped transforms used in perceptual audio coding. This allows for an invertible integer-to-integer approximation of the original transform, e.g. the IntMDCT as an integer approximation of the MDCT. The same technique can also be applied to low-delay filter banks. A generalized, multi-dimensional lifting approach and a noise-shaping technique are introduced, allowing to further optimize the accuracy of the approximation to the original transform. Based on these new integer transforms, this work presents new audio coding schemes and applications. The audio coding applications cover lossless audio coding, scalable lossless enhancement of a perceptual audio coder and fine-grain scalable perceptual and lossless audio coding. Finally an approach to data hiding with high data rates in uncompressed audio signals based on integer transforms is described

Frequency-warped autoregressive modeling and filtering

This thesis consists of an introduction and nine articles. The articles are related to the application of frequency-warping techniques to audio signal processing, and in particular, predictive coding of wideband audio signals. The introduction reviews the literature and summarizes the results of the articles. Frequency-warping, or simply warping techniques are based on a modification of a conventional signal processing system so that the inherent frequency representation in the system is changed. It is demonstrated that this may be done for basically all traditional signal processing algorithms. In audio applications it is beneficial to modify the system so that the new frequency representation is close to that of human hearing. One of the articles is a tutorial paper on the use of warping techniques in audio applications. Majority of the articles studies warped linear prediction, WLP, and its use in wideband audio coding. It is proposed that warped linear prediction would be particularly attractive method for low-delay wideband audio coding. Warping techniques are also applied to various modifications of classical linear predictive coding techniques. This was made possible partly by the introduction of a class of new implementation techniques for recursive filters in one of the articles. The proposed implementation algorithm for recursive filters having delay-free loops is a generic technique. This inspired to write an article which introduces a generalized warped linear predictive coding scheme. One example of the generalized approach is a linear predictive algorithm using almost logarithmic frequency representation.reviewe

Scalable and perceptual audio compression

This thesis deals with scalable perceptual audio compression. Two scalable perceptual solutions as well as a scalable to lossless solution are proposed and investigated. One of the scalable perceptual solutions is built around sinusoidal modelling of the audio signal whilst the other is built on a transform coding paradigm. The scalable coders are shown to scale both in a waveform matching manner as well as a psychoacoustic manner. In order to measure the psychoacoustic scalability of the systems investigated in this thesis, the similarity between the original signal\u27s psychoacoustic parameters and that of the synthesized signal are compared. The psychoacoustic parameters used are loudness, sharpness, tonahty and roughness. This analysis technique is a novel method used in this thesis and it allows an insight into the perceptual distortion that has been introduced by any coder analyzed in this manner