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In this work, we investigate a hybrid decoding approach that combines algebraic hard-input decoding of binary block codes with soft-input decoding. In particular, an acceptance criterion is proposed which determines the reliability of a candidate codeword. For many received codewords the stopping criterion indicates that the hard-decoding result is sufficiently reliable, and the costly soft-input decoding can be omitted. The proposed acceptance criterion significantly reduces the decoding complexity. For simulations we combine the algebraic hard-input decoding with ordered statistics decoding, which enables near maximum likelihood soft-input decoding for codes of small to medium block lengths.
The reliability of flash memories suffers from various error causes. Program/erase cycles, read disturb, and cell to cell interference impact the threshold voltages and cause bit errors during the read process. Hence, error correction is required to ensure reliable data storage. In this work, we investigate the bit-labeling of triple level cell (TLC) memories. This labeling determines the page capacities and the latency of the read process. The page capacity defines the redundancy that is required for error correction coding. Typically, Gray codes are used to encode the cell state such that the codes of adjacent states differ in a single digit. These Gray codes minimize the latency for random access reads but cannot balance the page capacities. Based on measured voltage distributions, we investigate the page capacities and propose a labeling that provides a better rate balancing than Gray labeling.
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.
The encoding of antenna patterns with generalized spatial modulation as well as other index modulation techniques require w-out-of-n encoding where all binary vectors of length n have the same weight w. This constant-weight property cannot be obtained by conventional linear coding schemes. In this work, we propose a new class of constant-weight codes that result from the concatenation of convolutional codes with constant-weight block codes. These constant-weight convolutional codes are nonlinear binary trellis codes that can be decoded with the Viterbi algorithm. Some constructed constant-weight convolutional codes are optimum free distance codes. Simulation results demonstrate that the decoding performance with Viterbi decoding is close to the performance of the best-known linear codes. Similarly, simulation results for spatial modulation with a simple on-off keying show a significant coding gain with the proposed coded index modulation scheme.
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.
Spatial modulation (SM) is a low-complexity multiple-input/multiple-output transmission technique that combines index modulation and quadrature amplitude modulation for wireless communications. In this work, we consider the problem of link adaption for generalized spatial modulation (GSM) systems that use multiple active transmit antennas simultaneously. Link adaption algorithms require a real-time estimation of the link quality of the time-variant communication channels, e.g., by means of estimating the mutual information. However, determining the mutual information of SM is challenging because no closed-form expressions have been found so far. Recently, multilayer feedforward neural networks were applied to compute the achievable rate of an index modulation link. However, only a small SM system with two transmit and two receive antennas was considered. In this work, we consider a similar approach but investigate larger GSM systems with multiple active antennas. 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.
Reliability is a crucial aspect of non-volatile NAND flash memories, and it is essential to thoroughly analyze the channel to prevent errors and ensure accurate readout. Es-timating the read reference voltages (RRV s) is a significant challenge due to the multitude of physical effects involved. The question arises which features are useful and necessary for the RRV estimation. Various possible features require specialized hardware or specific readout techniques to be usable. In contrast we consider sparse histograms based on the decision thresholds for hard-input and soft-input decoding. These offer a distinct advantage as they are derived directly from the raw readout data without the need for decoding. This paper focuses on the information-theoretic study of different features, especially on the exploration of the mutual information (MI) between feature vector and RRV. In particular, we investigate the dependency of the MI on the resolution of the histograms. With respect to the RRV estimation, sparse histograms provide sufficient information for near-optimum estimation.
List decoding for concatenated codes based on the Plotkin construction with BCH component codes
(2021)
Reed-Muller codes are a popular code family based on the Plotkin construction. Recently, these codes have regained some interest due to their close relation to polar codes and their low-complexity decoding. We consider a similar code family, i.e., the Plotkin concatenation with binary BCH component codes. This construction is more flexible regarding the attainable code parameters. In this work, we consider a list-based decoding algorithm for the Plotkin concatenation with BCH component codes. The proposed list decoding leads to a significant coding gain with only a small increase in computational complexity. Simulation results demonstrate that the Plotkin concatenation with the proposed decoding achieves near maximum likelihood decoding performance. This coding scheme can outperform polar codes for moderate code lengths.
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.