Multi-Stage Quantum Turbo Codes with an Arbitrary Small Decoding Error Probability

Jean–Pierre Tillich

Jeong W. Lee, Rudiger L. Urbanke, Richard E. Blahut

In this correspondence, the stopping set of turbo codes with iterative decoding in the binary erasure channel is defined. Block and bit erasure probabilities of turbo codes are studied by using the stopping set analysis. It is found that block and bit erasure probabilities of turbo codes with iterative decoding are higher than those with maximum-likelihood decoding, where the differences are negligible in the error floor region. It is shown that in the error floor region, block and bit erasure probabilities of turbo codes with iterative decoding are dominated by small stopping sets and are asymptotically dominated by low weight codewords.

郭大波 Guo Dabo, 张宁 Zhang Ning, 刘纲 LIU Gang

Two legitimate users of an encryption system,Alice and Bob,want to acquire the key from the related Gaussian continuous variables X and Y transferred through a quantum channel,by exchanging parts of information through an ideal public authorized channel,and they get consistent binary keys from the inconsistent X and Y.This process is referred to reconciliation.This paper builds a reconciliation scheme for continuous-variables quantum key distribution using Turbo codes as the primitive code,on the basis of Sliced Error Correction(SEC) and Multi Level coding/Multi Stage Decoding(MLC/MSD).Parity bits of Turbo code are employed as the redundant information in the Slepian-Wolf encoding and decoding scheme.The simulation results show that the reconciliation convergences when the SNR is 7dB above whilst the block size is 20000.

Iñiguez de Gordoa Pouso

Mohd Azri Mohd Izhar, Zunaira Babar, Hung Viet Nguyen +5 more

Inspired by the success of classical turbo codes, quantum turbo codes (QTCs) have also been conceived for near-hashing-bound transmission of quantum information over memoryless quantum channels. However, in real physical situations, the memoryless channel assumption may not be well justified, since the channel often exhibits memory of previous error events. Here, we investigate the performance of QTCs over depolarizing channels exhibiting memory and we show that they suffer from a performance degradation at low depolarizing probability values. In order to circumvent the performance degradation issue, we conceive a new coding scheme termed quantum turbo coding scheme exploiting error-correlation (QTC-EEC) that is capable of utilizing the error-correlation while performing the iterative decoding at the receiver. The proposed QTC-EEC can achieve convergence threshold at a higher depolarizing probability for channels with a higher value of correlation parameter and achieve performance near to the capacity. Finally, we propose a joint decoding and estimation scheme for our QTC-EEC relying on the correlation estimation (QTC-EEC-E) designed for more realistic quantum systems with unknown correlation parameter. Simulation results reveal that the proposed QTC-EEC-E can achieve the same performance as that of the ideal system of known correlation parameter and hence demonstrate the accurate estimation of the proposed QTC-EEC-E.

Sajed Sajed