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This work investigates soft input decoding for generalized concatenated (GC) codes. The GC codes are constructed from inner nested binary Bose-Chaudhuri-Hocquenghem (BCH)codes and outer Reed-Solomon (RS) codes. In order to enable soft input decoding for the inner BCH block codes, a sequential stack decoding algorithm is used. Ordinary stack decoding of binary block codes requires the complete trellis of the code.
In this work a representation of the block codes based on the trellises of supercodes is proposed in order to reduce the memory requirements for the representation of the BCH codes. Results for the decoding performance of the overall GC code are presented.
Furthermore, an efficient hardware implementation of the GC decoder is proposed.
Codes over quotient rings of Lipschitz integers have recently attracted some attention. This work investigates the performance of Lipschitz integer constellations for transmission over the AWGN channel by means of the constellation figure of merit. A construction of sets of Lipschitz integers is presented that leads to a better constellation figure of merit compared to ordinary Lipschitz integer constellations. In particular, it is demonstrated that the concept of set partitioning can be applied to quotient rings of Lipschitz integers where the number of elements is not a prime number. It is shown that it is always possible to partition such quotient rings into additive subgroups in a manner that the minimum Euclidean distance of each subgroup is strictly larger than in the original set. The resulting signal constellations have a better performance for transmission over an additive white Gaussian noise channel compared to Gaussian integer constellations and to ordinary Lipschitz integer constellations.
This contribution presents a data compression scheme for applications in non-volatile flash memories. The objective of the data compression algorithm is to reduce the amount of user data such that the redundancy of the error correction coding can be increased in order to improve the reliability of the data storage system. The data compression is performed on block level considering data blocks of 1 kilobyte. We present an encoder architecture that has low memory requirements and provides a fast data encoding.
This work proposes an efficient hardware Implementation of sequential stack decoding of binary block codes. The decoder can be applied for soft input decoding for generalized concatenated (GC) codes. The GC codes are constructed from inner nested binary Bose-Chaudhuri-Hocquenghem (BCH) codes and outer Reed-Solomon (RS) codes. In order to enable soft input decoding for the inner BCH block codes, a sequential stack decoding algorithm is used.
This work investigates data compression algorithms for applications in non-volatile flash memories. The main goal of the data compression is to minimize the amount of user data such that the redundancy of the error correction coding can be increased and the reliability of the error correction can be improved. A compression algorithm is proposed that combines a modified move-to-front algorithm with Huffman coding. The proposed data compression algorithm has low complexity, but provides a compression gain comparable to the Lempel-Ziv-Welch algorithm.
In this paper we propose a method to determine the active speaker for each time-frequency point in the noisy signals of a microphone array. This detection is based on a statistical model where the speech signals as well as noise signals are assumed to be multivariate Gaussian random variables in the Fourier domain. Based on this model we derive a maximum-likelihood detector for the active speaker. The decision is based on the a posteriori signal to noise ratio (SNR) of a speaker dependent max-SNR beamformer.
This paper studies suitable models for the identification of nonlinear acoustic systems. A cascaded structure of nonlinear filters is proposed that contains several parallel branches, consisting of polynomial functions followed by a linear filter for each order of nonlinearity. The second order of nonlinearity is additionally modelled with a parallel branch, containing a Volterra filter. These are followed by a long linear FIR filter that is able to model the room acoustics. The model is applied to the identification of a tube power amplifier feeding a guitar loudspeaker cabinet in an acoustic room. The adaptive identification is performed by the normalized least mean square (NLMS) algorithm. Compared with a generalized polynomial Hammerstein (GPH) model, the accuracy in modelling the dedicated real world system can be improved to a greater extend than increasing the order of nonlinearity in the GPH model.
This work proposes a decoder implementation for high-rate generalized concatenated (GC) codes. The proposed codes are well suited for error correction in flash memories for high reliability data storage. The GC codes are constructed from inner extended binary Bose-Chaudhuri-Hocquenghem (BCH) codes and outer Reed-Solomon (RS) codes. The extended BCH codes enable high-rate GC codes. Moreover, the decoder can take advantage of soft information. For the first three levels of inner codes we propose an optional Chase soft decoder. In this work, the code construction is explained and a decoder architecture is presented. Furthermore, area and throughput results are discussed.
In diesem Beitrag wird die Hardware-Implementierung eines Datenkompressionsverfahrens auf einem FPGA vorgestellt. Das Verfahren wurde speziell für Kompression kurzer Datenblöcke in Flash-Speichern entwickelt. Dabei werden Quelldaten mithilfe eines Encoders komprimiert und mit einem Decoder verlustlos dekomprimiert. Durch die Reduktion der Datenrate kann in Flash-Speichern die Übertragungsdauer zum Lesen und Schreiben reduziert werden. Ebenso ist eine Kompression von Nutzdaten sinnvoll, um zusätzliche Redundanzen für einen Fehlerschutz einfügen zu können, ohne den Gesamtspeicherplatzbedarf zu erhöhen.
The binary asymmetric channel (BAC) is a model for the error characterization of multi-level cell (MLC) flash memories. This contribution presents a joint channel and source coding approach improving the reliability of MLC flash memories. The objective of the data compression algorithm is to reduce the amount of user data such that the redundancy of the error correction coding can be increased in order to improve the reliability of the data storage system. Moreover, data compression can be utilized to exploit the asymmetry of the channel to reduce the error probability. With MLC flash memories data compression has to be performed on block level considering short data blocks. We present a coding scheme suitable for blocks of 1 kilobyte of data.
Error correction coding based on soft-input decoding can significantly improve the reliability of flash memories. Such soft-input decoding algorithms require reliability information about the state of the memory cell. This work proposes a channel model for soft-input decoding that considers the asymmetric error characteristic of multi-level cell (MLC) and triple-level cell (TLC) memories. Based on this model, an estimation method for the channel state information is devised which avoids additional pilot data for channel estimation. Furthermore, the proposed method supports page-wise read operations.
Generalized concatenated (GC) codes with soft-input decoding were recently proposed for error correction in flash memories. This work proposes a soft-input decoder for GC codes that is based on a low-complexity bit-flipping procedure. This bit-flipping decoder uses a fixed number of test patterns and an algebraic decoder for soft-input decoding. An acceptance criterion for the final candidate codeword is proposed. Combined with error and erasure decoding of the outer Reed-Solomon codes, this bit-flipping decoder can improve the decoding performance and reduce the decoding complexity compared to the previously proposed sequential decoding. The bit-flipping decoder achieves a decoding performance similar to a maximum likelihood decoder for the inner codes.
This work proposes a construction for low-density parity-check (LDPC) codes over finite Gaussian integer fields. Furthermore, a new channel model for codes over Gaussian integers is introduced and its channel capacity is derived. This channel can be considered as a first order approximation of the additive white Gaussian noise channel with hard decision detection where only errors to nearest neighbors in the signal constellation are considered. For this channel, the proposed LDPC codes can be decoded with a simple non-probabilistic iterative decoding algorithm similar to Gallager's decoding algorithm A.
Digitale Signaturen zum Überprüfen der Integrität von Daten, beispielsweise von Software-Updates, gewinnen zunehmend an Bedeutung. Im Bereich der eingebetteten Systeme kommen derzeit wegen der geringen Komplexität noch überwiegend symmetri-sche Verschlüsselungsverfahren zur Berechnung eines Authentifizierungscodes zum Einsatz. Asym-metrische Kryptosysteme sind rechenaufwendiger, bieten aber mehr Sicherheit, weil der Schlüssel zur Authentifizierung nicht geheim gehalten werden muss. Asymmetrische Signaturverfahren werden typischerweise zweistufig berechnet. Der Schlüssel wird nicht direkt auf die Daten angewendet, sondern auf deren Hash-Wert, der mit Hilfe einer Hash-funktion zuvor berechnet wurde. Zum Einsatz dieser Verfahren in eingebetteten Systemen ist es erforder-lich, dass die Hashfunktion einen hinreichend gro-ßen Datendurchsatz ermöglicht. In diesem Beitrag wird eine effiziente Hardware-Implementierung der SHA-256 Hashfunktion vorgestellt.
This work introduces new signal constellations based on Eisenstein integers, i.e., the hexagonal lattice. These sets of Eisenstein integers have a cardinality which is an integer power of three. They are proposed as signal constellations for representation in the equivalent complex baseband model, especially for applications like physical-layer network coding or MIMO transmission where the constellation is required to be a subset of a lattice. It is shown that these constellations form additive groups where the addition over the complex plane corresponds to the addition with carry over ternary Galois fields. A ternary set partitioning is derived that enables multilevel coding based on ternary error-correcting codes. In the subsets, this partitioning achieves a gain of 4.77 dB, which results from an increased minimum squared Euclidean distance of the signal points. Furthermore, the constellation-constrained capacities over the AWGN channel and the related level capacities in case of ternary multilevel coding are investigated. Simulation results for multilevel coding based on ternary LDPC codes are presented which show that a performance close to the constellation-constrained capacities can be achieved.
The computational complexity of the optimal maximum likelihood (ML) detector for spatial modulation increases rapidly as more transmit antennas or larger modulation orders are employed. Hence, ML detection may be infeasible for higher bit rates. This work proposes an improved suboptimal detection algorithm based on the Gaussian approximation method. It is demonstrated that the new method is closely related to the previously published signal vector based detection and the modified maximum ratio combiner, but can improve the detection performance compared to these methods. Furthermore, the performance of different signal constellations with suboptimal detection is investigated. Simulation results indicate that the performance loss compared to ML detection depends heavily on the signal constellation, where the recently proposed Eisenstein integer constellations are beneficial compared to classical QAM or PSK constellations.