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In this letter, we present an approach to building a new generalized multistream spatial modulation system (GMSM), where the information is conveyed by the two active antennas with signal indices and using all possible active antenna combinations. The signal constellations associated with these antennas may have different sizes. In addition, four-dimensional hybrid frequency-phase modulated signals are utilized in GMSM. Examples of GMSM systems are given and computer simulation results are presented for transmission over Rayleigh and deep Nakagami- m flat-fading channels when maximum-likelihood detection is used. The presented results indicate a significant improvement of characteristics compared to the best-known similar systems.
Code-based cryptosystems are promising candidates for post-quantum cryptography. Recently, generalized concatenated codes over Gaussian and Eisenstein integers were proposed for those systems. For a channel model with errors of restricted weight, those q-ary codes lead to high error correction capabilities. Hence, these codes achieve high work factors for information set decoding attacks. In this work, we adapt this concept to codes for the weight-one error channel, i.e., a binary channel model where at most one bit-error occurs in each block of m bits. We also propose a low complexity decoding algorithm for the proposed codes. Compared to codes over Gaussian and Eisenstein integers, these codes achieve higher minimum Hamming distances for the dual codes of the inner component codes. This property increases the work factor for a structural attack on concatenated codes leading to higher overall security. For comparable security, the key size for the proposed code construction is significantly smaller than for the classic McEliece scheme based on Goppa codes.
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.
The code-based McEliece cryptosystem is a promising candidate for post-quantum cryptography. The sender encodes a message, using a public scrambled generator matrix, and adds a random error vector. In this work, we consider q-ary codes and restrict the Lee weight of the added error symbols. This leads to an increased error correction capability and a larger work factor for information-set decoding attacks. In particular, we consider codes over an extension field and use the one-Lee error channel, which restricts the error values to Lee weight one. For this channel model, generalized concatenated codes can achieve high error correction capabilities. We discuss the decoding of those codes and the possible gain for decoding beyond the guaranteed error correction capability.
Mutual Information Analysis for Generalized Spatial Modulation Systems With Multilevel Coding
(2022)
Generalized Spatial Modulation (GSM) enables a trade-off between very high spectral efficiencies and low hardware costs for massive MIMO systems. This is achieved by transmitting information via the selection of active antennas from a set of available antennas besides the transmission of conventional data symbols. GSM systems have been investigated concerning various aspects like suitable signal constellations, efficient detection algorithms, hardware implementations, spatial precoding, and error control coding. On the other hand, determining the capacity of GSM is challenging because no closed-form expressions have been found so far. This paper investigates the mutual information for different GSM variants. We consider a multilevel coding approach, where the antenna selection and IQ modulation are encoded independently. Combined with multistage decoding, such an approach enables low-complexity capacity-achieving coded modulation. The influence of the data symbols on the mutual information is illuminated. We analyze the portions of mutual information related to antenna selection and the IQ modulation processes which depend on the GSM variant and the signal constellation. Moreover, the potential of spatial modulation for massive MIMO systems with many transmit antennas is investigated. Especially in systems with many transmit antennas much information can be conveyed by antenna selection.
The growing error rates of triple-level cell (TLC) and quadruple-level cell (QLC) NAND flash memories have led to the application of error correction coding with soft-input decoding techniques in flash-based storage systems. Typically, flash memory is organized in pages where the individual bits per cell are assigned to different pages and different codewords of the error-correcting code. This page-wise encoding minimizes the read latency with hard-input decoding. To increase the decoding capability, soft-input decoding is used eventually due to the aging of the cells. This soft-decoding requires multiple read operations. Hence, the soft-read operations reduce the achievable throughput, and increase the read latency and power consumption. In this work, we investigate a different encoding and decoding approach that improves the error correction performance without increasing the number of reference voltages. We consider TLC and QLC flashes where all bits are jointly encoded using a Gray labeling. This cell-wise encoding improves the achievable channel capacity compared with independent page-wise encoding. Errors with cell-wise read operations typically result in a single erroneous bit per cell. We present a coding approach based on generalized concatenated codes that utilizes this property.
Large persistent memory is crucial for many applications in embedded systems and automotive computing like AI databases, ADAS, and cutting-edge infotainment systems. Such applications require reliable NAND flash memories made for harsh automotive conditions. However, due to high memory densities and production tolerances, the error probability of NAND flash memories has risen. As the number of program/erase cycles and the data retention times increase, non-volatile NAND flash memories' performance and dependability suffer. The read reference voltages of the flash cells vary due to these aging processes. In this work, we consider the issue of reference voltage adaption. The considered estimation procedure uses shallow neural networks to estimate the read reference voltages for different life-cycle conditions with the help of histogram measurements. We demonstrate that the training data for the neural networks can be enhanced by using shifted histograms, i.e., a training of the neural networks is possible based on a few measurements of some extreme points used as training data. The trained neural networks generalize well for other life-cycle conditions.
Automotive computing applications like AI databases, ADAS, and advanced infotainment systems have a huge need for persistent memory. This trend requires NAND flash memories designed for extreme automotive environments. However, the error probability of NAND flash memories has increased in recent years due to higher memory density and production tolerances. Hence, strong error correction coding is needed to meet automotive storage requirements. Many errors can be corrected by soft decoding algorithms. However, soft decoding is very resource-intensive and should be avoided when possible. NAND flash memories are organized in pages, and the error correction codes are usually encoded page-wise to reduce the latency of random reads. This page-wise encoding does not reach the maximum achievable capacity. Reading soft information increases the channel capacity but at the cost of higher latency and power consumption. In this work, we consider cell-wise encoding, which also increases the capacity compared to page-wise encoding. We analyze the cell-wise processing of data in triple-level cell (TLC) NAND flash and show the performance gain when using Low-Density Parity-Check (LDPC) codes. In addition, we investigate a coding approach with page-wise encoding and cell-wise reading.
Reed-Muller (RM) codes have recently regained some interest in the context of low latency communications and due to their relation to polar codes. RM codes can be constructed based on the Plotkin construction. In this work, we consider concatenated codes based on the Plotkin construction, where extended Bose-Chaudhuri-Hocquenghem (BCH) codes are used as component codes. This leads to improved code parameters compared to RM codes. Moreover, this construction is more flexible concerning the attainable code rates. Additionally, new soft-input decoding algorithms are proposed that exploit the recursive structure of the concatenation and the cyclic structure of the component codes. First, we consider the decoding of the cyclic component codes and propose a low complexity hybrid ordered statistics decoding algorithm. Next, this algorithm is applied to list decoding of the Plotkin construction. The proposed list decoding approach achieves near-maximum-likelihood performance for codes with medium lengths. The performance is comparable to state-of-the-art decoders, whereas the complexity is reduced.