In particular, the SNR range of positive secrecy rate increases by 1.44 times, and the maximum secret key rate improves by 2.10 times as compared to the existing design rules. The performance improvements are confirmed by comparing complexities and secret key rates of IR schemes with MET-LDPC codes whose ensembles are optimized with the proposed and existing design rules. The rate compatibility and the improved error-rate performances significantly enhance the efficiency of IR for CV-QKD systems.
Thus, the proposed design rule allows one to implement rate-compatible MET-LDPC codes with good performances both in the threshold and low-error-rate regions. In addition to the rate compatibility, the design rule effectively resolves the high error-floor issue which has been known as a technical challenge of MET-LDPC codes at low rates. That means according to the rule t < d, that this code can detect only a t-bit error, which means 1 ( but that's not true, because it can detect 3 bit erros).In this paper, we propose a design rule of rate-compatible punctured multi-edge type low-density parity-check (MET-LDPC) code ensembles with degree-one variable nodes for the information reconciliation (IR) of continuous-variable quantum key distribution (CV-QKD) systems. The numbers behind the 'bars/underscores' are the parity-check bits, it means that in each column/row is even count of number 1. T < d (and d stands for hamming distance, its minimum distance between the 2 code words / t stands for t-bit errors). The second thing is, we were learning about hamming distance and there is a rule, which says that block code finds t-bit error when this equation is right: I think the two-dimensional parity check does finds 3-bit erros, but it can't (in every case) correct it. I was given a homework, in which I should explain how does the two dimensional parity check finds 3-bit errors.
I am little bit confused right now, in the school we were learning about Hamming's code, Block codes etc.
Firstly, I would like to apologize if I misplaced this topic / i think the theory of coding is close to CS /
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