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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.
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 that leads to a better constellation figure of merit compared to ordinary Lipschitz integer constellations is presented. 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. In addition, we present multilevel code constructions for the new signal constellations.
This paper proposes a pipelined decoder architecture for generalised concatenated (GC) codes. These codes are constructed from inner binary Bose-Chaudhuri-Hocquenghem (BCH) and outer Reed-Solomon codes. The decoding of the component codes is based on hard decision syndrome decoding algorithms. The concatenated code consists of several small BCH codes. This enables a hardware architecture where the decoding of the component codes is pipelined. A hardware implementation of a GC decoder is presented and the cell area, cycle counts as well as the timing constraints are investigated. The results are compared to a decoder for long BCH codes with similar error correction performance. In comparison, the pipelined GC decoder achieves a higher throughput and has lower area consumption.
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.
Four-Dimensional Hurwitz Signal Constellations, Set Partitioning, Detection, and Multilevel Coding
(2021)
The Hurwitz lattice provides the densest four-dimensional packing. This fact has motivated research on four-dimensional Hurwitz signal constellations for optical and wireless communications. This work presents a new algebraic construction of finite sets of Hurwitz integers that is inherently accompanied by a respective modulo operation. These signal constellations are investigated for transmission over the additive white Gaussian noise (AWGN) channel. It is shown that these signal constellations have a better constellation figure of merit and hence a better asymptotic performance over an AWGN channel when compared with conventional signal constellations with algebraic structure, e.g., two-dimensional Gaussian-integer constellations or four-dimensional Lipschitz-integer constellations. We introduce two concepts for set partitioning of the Hurwitz integers. The first method is useful to reduce the computational complexity of the symbol detection. This suboptimum detection approach achieves near-maximum-likelihood performance. In the second case, the partitioning exploits the algebraic structure of the Hurwitz signal constellations. We partition the Hurwitz integers into additive subgroups in a manner that the minimum Euclidean distance of each subgroup is larger than in the original set. This enables multilevel code constructions for the new signal constellations.
Code-based cryptography is a promising candidate for post-quantum public-key encryption. The classic McEliece system uses binary Goppa codes, which are known for their good error correction capability. However, the key generation and decoding procedures of the classic McEliece system have a high computation complexity. Recently, q-ary concatenated codes over Gaussian integers were proposed for the McEliece cryptosystem together with the one-Mannheim error channel, where the error values are limited to Mannheim weight one. For this channel, concatenated codes over Gaussian integers achieve a higher error correction capability than maximum distance separable (MDS) codes with bounded minimum distance decoding. This improves the work factor regarding decoding attacks based on information-set decoding. This work proposes an improved construction for codes over Gaussian integers. These generalized concatenated codes extent the rate region where the work factor is beneficial compared to MDS codes. They allow for shorter public keys for the same level of security as the classic Goppa codes. Such codes are beneficial for lightweight code-based cryptosystems.
Large-scale quantum computers threaten today's public-key cryptosystems. The code-based McEliece and Niederreiter cryptosystems are among the most promising candidates for post-quantum cryptography. Recently, a new class of q-ary product codes over Gaussian integers together with an efficient decoding algorithm were proposed for the McEliece cryptosystems. It was shown that these codes achieve a higher work factor for information-set decoding attacks than maximum distance separable (MDS) codes with comparable length and dimension. In this work, we adapt this q-ary product code construction to codes over Eisenstein integers. We propose a new syndrome decoding method which is applicable for Niederreiter cryptosystems. The code parameters and work factors for information-set decoding are comparable to codes over Gaussian integers. Hence, the new construction is not favorable for the McEliece system. Nevertheless, it is beneficial for the Niederreiter system, where it achieves larger message lengths. While the Niederreiter and McEliece systems have the same level of security, the Niederreiter system can be advantageous for some applications, e.g., it enables digital signatures. The proposed coding scheme is interesting for lightweight Niederreiter cryptosystems and embedded security due to the short code lengths and low decoding complexity.
Acoustic Echo Cancellation (AEC) plays a crucial role in speech communication devices to enable full-duplex communication. AEC algorithms have been studied extensively in the literature. However, device specific details like microphone or loudspeaker configurations are often neglected, despite their impact on the echo attenuation or near-end speech quality. In this work, we propose a method to investigate different loudspeaker-microphone configurations with respect to their contribution to the overall AEC performance. A generic AEC system consisting of an adaptive filter and a Wiener post filter is used for a fair comparison between different setups. We propose the near-end-to-residual-echo ratio (NRER) and the attenuation-of-near-end (AON) as quality measures for the full-duplex AEC performance.
