吉田 雅一

We introduce a quantum key distribution protocol using mean multi-kings’ problem. Using this protocol, a sender can share a bit sequence as a secret key with receivers. We consider a relation between information gain by an eavesdropper and disturbance contained in legitimate users’ information. In BB84 protocol, such relation is known as the so-called information disturbance theorem. We focus on a setting that the sender and two receivers try to share bit sequences and the eavesdropper tries to extract information by interacting legitimate users’ systems and an ancilla system. We derive trade-off inequalities between distinguishability of quantum states corresponding to the bit sequence for the eavesdropper and error probability of the bit sequence shared with the legitimate users. Our inequalities show that eavesdropper’s extracting information regarding the secret keys inevitably induces disturbing the states and increasing the error probability.

Spatially-coupled irregular LDPC codes by non square superposition matrices are proposed. Starting with a binary base matrix and replacing non-zero entries in the base matrix by superposition matrices produces a parity-check matrix and its corresponding code ensemble. The proposed codes have two features: a) flexible code rates because the size of the superposition matrix is arbitrarily adjusted, and b) guaranteed iterative decoding performance because the degree distributions of the superposition matrix are optimized, even in a finite coupling width. The numerical analysis of density evolution and Monte-Carlo simulations show that our proposed code ensembles approach the Shannon limits at arbitrary code rates and outperform the conventional codes.

This paper considers spatially coupled repeat accumulate (SC-RA) coded interleave-division multiple-access (IDMA) systems with segmented interleavers. Each user employs an SC-RA encoder and a spreader followed by user-specific segmented interleavers. Each segment corresponds with a parity variable node in the SC-RA code's protograph. Since all the users' parity bits at the ends of the coupling positions are synchronously superimposed in segments, the extrinsic messages to the sum node are totally enhanced in the iterative decoding. Density evolution (DE) with Gaussian approximation (GA) shows that the belief propagation threshold of the proposed system approaches closer to the Shannon limit than systems without segmentation and the conventional RA-IDMA systems.

A K-user nonbinary parallel concatenated code (PCC) is proposed for a Gaussian MAC with symbol synchronization, equal-power, and equal-rate users. In a K-user q-ary PCC over finite field GF(q), each user employs a parallel concatenated code, with a rate-(1/r) q-ary repetition component code and M rate-1 q-ary accumulation component codes. Employing q-ary repetition code is to overcome the multi-user interference and also provide coding gain. The K-user q-ary PCC is not only rate compatible, but also with very low encoding and decoding complexities due to employing such simple component codes. An EXIT chart analysis is given to estimate the decoding threshold of the K-user q-ary PCC. Numerical results show that the decoding threshold of K-user q-ary PCC improves as the field order q increases. The 10-user 64-ary PCC improves the decoding threshold by 1.88 dB over the binary case. The decoding threshold of 15-user 64-ary PCC at sum rate 3/4 is only 0.75 dB away from the Shannon bound. Bit-error-rate simulations are provided to verify the analysis.

Entangled states play crucial roles in quantum information theory and its applied technologies. In various protocols such as quantum teleportation and quantum key distribution, a good entangled state shared by a pair of distant players is indispensable. In this paper, we numerically examine entanglement sharing protocols using quantum LDPC CSS codes. The sum-product decoding method enables us to detect uncorrectable errors, and thus, two protocols, Detection and Resending (DR) protocol and Non-Detection (ND) protocol are considered. In DR protocol, the players abort the protocol and repeat it if they detect the uncorrectable errors, whereas in ND protocol they do not abort the protocol. We show that DR protocol yields smaller error rate than ND protocol. In addition, it is shown that rather high reliability can be achieved by DR protocol with quantum LDPC CSS codes.