Soft decoding of short/medium length codes using ordered statistics for quantum key distribution

Quantum key distribution (QKD) is a cryptographic communication protocol that utilizes quantum mechanical properties for provable absolute security against an eavesdropper. The communication is carried between two terminals using random photon polarization states represented through quantum states. Both these terminals are interconnected through disjoint quantum and classical channels. Information reconciliation using delay controlled joint decoding is performed at the receiving terminal. Its performance is characterized using data and error rates. Achieving low error rates is particularly challenging for schemes based on error correcting codes with short code lengths. This article addresses the decoding process using ordered statistics decoding for information reconciliation of both short and medium length Bose–Chaudhuri–Hocquenghem codes over a QKD link. The link’s quantum channel is modeled as a binary symmetric quantum depolarization channel, whereas the classical channel is configured with additive white Gaussian noise. Our results demonstrate the achievement of low bit error rates, and reduced decoding complexity when compared to other capacity achieving codes of similar length and configuration.

Upgrading an Analog Recovery Loop for Optimized Decoding Jointly to an Increased data-Rate

The maximum likelihood detection theory improves the error-rate of a sub-optimal but cheaper, coded symbol recovery loop using oversampling proposed as an alternate solution for the decoding problem without the log-likelihood ratio computation. The former implementation delivers the output data in one-symbol delay, and the required transistor count makes this approach attractive for ultra-low-energy wireless applications. The proposed hardware upgrade includes an analog to digital converter and fixed-point accumulation logic to compute the soft values, replacing a trigger used as a hard detector. This work investigates the soft decoding in the presence of binary and non-binary source symbols. Simulation results show that the soft approach improves the signal-to-noise ratio by 3dB and 2.5 dB when the encoding rates are 1/3 and 2/3.

Soft Interference Cancellation for Random Coding in Massive Gaussian Multiple-Access

In 2017, Polyanskiy showed that the trade-off between power and bandwidth efficiency for massive Gaussian random access is governed by two fundamentally different regimes: low power and high power. For both regimes, tight performance bounds were found by Zadik et al., in 2019. This work utilizes recent results on the exact block error probability of Gaussian random codes in additive white Gaussian noise to propose practical methods based on iterative soft decoding to closely approach these bounds. In the low power regime, this work finds that orthogonal random codes can be applied directly. In the high power regime, a more sophisticated effort is needed. This work shows that power-profile optimization by means of linear programming, as pioneered by Caire et al. in 2001, is a promising strategy to apply. The proposed combination of orthogonal random coding and iterative soft decoding even outperforms the existence bounds of Zadik et al. in the low power regime and is very close to the non-existence bounds for message lengths around 100 and above. Finally, the approach of power optimization by linear programming proposed for the high power regime is found to benefit from power imbalances due to fading which makes it even more attractive for typical mobile radio channels.

A Nonuniform Reference Voltage Optimization Based on Relative-Precision-Loss Ratios in MLC NAND Flash Memory

In Multi-Level-Cell (MLC) NAND flash memory, cell-to-cell interference (CCI) and retention time have become the main noise that degrades the data storage reliability. To mitigate such noise, a relative precision loss (RPL) nonuniform reference voltage sensing strategy is proposed in this paper. First, based on the NAND flash channel model with CCI and retention noise, we simulate the data storage process of MLC NAND flash by Monte Carlo method, and find that the threshold-voltage of each disturbed storage state shows approximately to be Gaussian distributed. Then, by Gaussian approximation, the distribution of threshold voltage can be estimated easily in mathematics with a little loss. Second, we introduce a concept of log-likelihood ratio (LLR)-based RPL ratio to determine the dominating overlap regions, and then propose a new nonuniform reference voltage sensing strategy. This strategy does not only reduce the memory sensing precision (i.e., the number of reference voltages), but also maintains the reliability of the soft information of NAND flash memory channel output for soft decoding. Third, we implement extensive simulations to verify the performance of the new nonuniform sensing strategy. The BER performances of LDPC codes for different sensing strategies are provided to show that the proposed LLR-based RPL-nonuniform sensing strategy can make a good compromise between memory sensing latency and error-correction performance.