ADVANCED ERROR CORRECTION METHOD USING LDPC CODES IN POST-PROCESSING STAGE IN QKD SYSTEMS
DOI:
https://doi.org/10.18372/2310-5461.51.15692Keywords:
QKD, LDPC, error correction, parity-check matrix, post-processingAbstract
This paper reviews the known error correction methods for QKD systems, identifies their advantages and disadvantages. The method of LDPC-codes is substantiated for improvement. Noise errors can occur when exchanging qubits between Alice and Bob through the quantum channel, and Bob may receive erroneous values when measuring states that need to be corrected in the post-processing phase. The verification matrix for LDPC codes is quasi-cyclic, ie each subsequent row of the matrix is cyclically shifted to the right by one bit relative to the previous row. This allows not only to describe the matrix only by the first line of the matrix, but also to use the property of isomorphism of circulating matrices with a ring of polynomials over the Galois field. That is, the verification matrix can be described by a certain polynomial. And the operations performed on this polynomial are applied to the matrix. Using such isomorphic properties of polynomials makes it much easier to create and store not only a test matrix but also a generating matrix, which avoids long-term matrix multiplications and the use of more memory to store matrix data, greatly simplifying hardware implementation. The code word is created by the method proposed by the author of LDPC-codes R. Gallagher. The decoding of code words in the original message uses a "soft" algorithm for spreading trust (belief-propagation algorithm) or sum-product algorithm (SPA), which has proven its effectiveness and is used in modern telecommunications systems. An algorithm for generating a verification matrix and an algorithm for generating a generating matrix based on the method for finding the inverse Euclidean-Wallis polynomial have been proposed and adapted for writing program code. Software has been created that implements the above algorithms, which can be found on the git repository
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