Quantum computing’s advancements pose a threat to conventional data encryption, but quantum key distribution (QKD) could be the solution. Continuous-variable quantum key distribution (CVQKD) is particularly promising for secure long-distance communication, but its practical implementation faces challenges, especially in the information reconciliation phase. This phase typically uses multi-edge type (MET) low-density parity-check (LDPC) codes, which have their own issues. Researchers Erdem Eray Cil and Laurent Schmalen propose a novel log-log domain sum-product algorithm (SPA) that reduces the precision of message representations by at least 25%, leading to a smaller memory footprint and lower resource consumption in hardware implementation.
Quantum Key Distribution and Information Reconciliation
Quantum computing has made significant strides in recent years, challenging the security of conventional data encryption schemes. A potential solution is quantum key distribution (QKD), which uses the laws of physics to generate and distribute secret keys for symmetric encryption. Among the various QKD techniques, continuous-variable quantum key distribution (CVQKD) has shown great potential for long-distance secure communication. However, the practical implementation of CVQKD faces several challenges, particularly in the information reconciliation phase, where the parties involved aim to extract a common raw key from their measurements.
The Role of LDPC Codes in CVQKD
This critical step typically employs multiedge type (MET) low-density parity-check (LDPC) codes, which require long code words and are sensitive to changes in decoding algorithms. Simplified belief propagation algorithms often exhibit suboptimal performance. The requirements of an LDPC decoder in long-distance CVQKD systems pose practical hardware challenges. To address these challenges, GPU-based decoders are commonly used due to their high parallelism and floating-point precision, which improve performance and throughput. However, these decoders have drawbacks such as high energy consumption and host dependence, limiting their commercial viability.
FPGA-based Decoders: An Alternative
As an alternative, FPGA-based decoders offer high parallel processing capabilities with lower energy consumption and host independence. However, CVQKD systems require high precision in the fixed-point representation of decoder messages, which increases the memory footprint of the decoder. To address this issue, a two-stage decoder architecture is proposed. By decreasing the fractional bit width, this architecture can reduce the memory footprint. However, it requires additional decoding iterations, leading to lower throughput.
The LogLog Domain SumProduct Algorithm
In this paper, Erdem Eray Cil and Laurent Schmalen from the Communications Engineering Lab at the Karlsruhe Institute of Technology propose a novel log-log domain sum-product algorithm (SPA) that reduces the precision of message representations by at least 25% without increasing the decoding iterations or decoding complexity compared to the conventional SPA. This algorithm leads to a smaller memory footprint and a lower resource consumption in hardware implementation.
Comparative Analysis of SPA and LogLog Domain SPA
The researchers offer a comparative analysis between SPA and log-log domain SPA, demonstrating the reduction in memory footprint achieved by the latter. Their results show that their algorithm achieves comparable or better decoding accuracy than the conventional SPA while saving at least 25% of the fractional bit width.
Forward Error Correction in CVQKD
QKD allows two parties, Alice and Bob, to establish a shared secret by exchanging and measuring quantum states while facing an adversary, Eve, who can access and manipulate the quantum channel. To generate a common bit string, which serves as raw key material, one of the parties uses forward error correction techniques to correct their string according to the other party’s string. This information reconciliation process is called reverse reconciliation when Alice corrects her string and direct reconciliation otherwise. For CVQKD, reverse reconciliation enables long-distance operation.
MultiEdge Type LDPC Codes for CVQKD
MET-LDPC codes with a cascade structure are suitable for long-distance CVQKD systems that operate in low SNR quantum channels as they can achieve near-capacity performance. These codes have a graph structure that consists of two subgraphs: one subgraph represents a high-rate code, and the other subgraph contains degree-1 variable nodes (VN) similar to low-density generator matrix codes. The connection between the subgraphs is established by specific optimized edges.
“Log-Log Domain Sum-Product Algorithm for Information Reconciliation in Continuous-Variable Quantum Key Distribution” by Erdem Cil and Laurent Schmalen, published on January 24, 2024. https://doi.org/10.48550/arxiv.2401.13748
