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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.
The introduction of multi level cell (MLC) and triple level cell (TLC) technologies reduced the reliability of flash memories significantly compared with single level cell (SLC) flash. The reliability of the flash memory suffers from various errors causes. Program/erase cycles, read disturb, and cell to cell interference impact the threshold voltages. With pre-defined fixed read thresholds a voltage shift increases the bit error rate (BER). This work proposes a read threshold calibration method that aims on minimizing the BER by adapting the read voltages. The adaptation of the read thresholds is based on the number of errors observed in the codeword protecting a small amount of meta-data. Simulations based on flash measurements demonstrate that this method can significantly reduce the BER of TLC memories.
Side Channel Attack Resistance of the Elliptic Curve Point Multiplication using Eisenstein Integers
(2020)
Asymmetric cryptography empowers secure key exchange and digital signatures for message authentication. Nevertheless, consumer electronics and embedded systems often rely on symmetric cryptosystems because asymmetric cryptosystems are computationally intensive. Besides, implementations of cryptosystems are prone to side-channel attacks (SCA). Consequently, the secure and efficient implementation of asymmetric cryptography on resource-constrained systems is demanding. In this work, elliptic curve cryptography is considered. A new concept for an SCA resistant calculation of the elliptic curve point multiplication over Eisenstein integers is presented and an efficient arithmetic over Eisenstein integers is proposed. Representing the key by Eisenstein integer expansions is beneficial to reduce the computational complexity and the memory requirements of an SCA protected implementation.
Side Channel Attack Resistance of the Elliptic Curve Point Multiplication using Gaussian Integers
(2020)
Elliptic curve cryptography is a cornerstone of embedded security. However, hardware implementations of the elliptic curve point multiplication are prone to side channel attacks. In this work, we present a new key expansion algorithm which improves the resistance against timing and simple power analysis attacks. Furthermore, we consider a new concept for calculating the point multiplication, where the points of the curve are represented as Gaussian integers. Gaussian integers are subset of the complex numbers, such that the real and imaginary parts are integers. Since Gaussian integer fields are isomorphic to prime fields, this concept is suitable for many elliptic curves. Representing the key by a Gaussian integer expansion is beneficial to reduce the computational complexity and the memory requirements of a secure hardware implementation.
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.
Soft-input decoding of concatenated codes based on the Plotkin construction and BCH component codes
(2020)
Low latency communication requires soft-input decoding of binary block codes with small to medium block lengths.
In this work, we consider generalized multiple concatenated (GMC) codes based on the Plotkin construction. These codes are similar to Reed-Muller (RM) codes. In contrast to RM codes, BCH codes are employed as component codes. This leads to improved code parameters. Moreover, a decoding algorithm is proposed that exploits the recursive structure of the concatenation. This algorithm enables efficient soft-input decoding of binary block codes with small to medium lengths. The proposed codes and their decoding achieve significant performance gains compared with RM codes and recursive GMC decoding.