In this correspondence, we study the minimum pseudo-weight and minimum pseudo-codewords of low-density parity-check (LDPC) codes under linear programming (LP) decoding. First, we show that the lower bound of Kelly, Sridhara, Xu and Rosenthal on the pseudo-weight of a pseudo-codeword of an LDPC code with girth greater than 4 is tight if and only if this pseudo-codeword is a real multiple of a co...

The speed at which two remote parties can exchange secret keys over a fixed-length fiber-optic cable in continuousvariable quantum key distribution (CV-QKD) is currently limited by the computational complexity of post-processing algorithms for key reconciliation. Multi-edge low-density paritycheck (LDPC) codes with low code rates and long block lengths were proposed for CV-QKD, in order to exte...

In this paper, we analyze the robustness for low-density parity-check (LDPC) codes over the Gilbert-Elliott (GE) channel. For this purpose we propose a density evolution method for the case where LDPC decoder uses the mismatched parameters for the GE channel. Using this method, we derive the region of tuples of true parameters and mismatched decoding parameters for the GE channel, where the dec...

We propose a new decoding algorithm of LDPC codes over the binary erasure channel (BEC). The proposed decoding algorithm is an iterative one which uses the sparseness structure of the parity-check matrix of LDPC codes. We show by simulation results that the proposed decoding algorithm and the conventional decoding algorithm have a trade-off between remaining erasure rate and complexity. Keyword...

In this correspondence, low-density parity-check (LDPC) codes are applied to lossy source coding and we study how the asymptotic performance of MacKay’s LDPC codes depends on the sparsity of the parity-check matrices in the source coding of the binary independent and identically distributed (i.i.d.) source with Pr = 1 = 0 5. In the sequel, it is shown that an LDPC code with column weight (log )...

In this work, we describe an LDPC code design framework for the unequal power two-user Gaussian multiple access channel using EXIT charts. We show that the sum-rate of the LDPC codes designed using our proposed method can get close to the maximal sum-rate of the two-user Gaussian multiple access channel. Moreover, we provide numerical simulation results that demonstrate the excellent finite-len...

Low-density parity-check (LDPC) codes characterized by minimum Hamming distances proportional to block sizes have been demonstrated. Like the codes mentioned in the immediately preceding article, the present codes are error-correcting codes suitable for use in a variety of wireless data-communication systems that include noisy channels. The previously mentioned codes have low decoding threshold...

Bias-tailoring allows quantum error correction codes to exploit qubit noise asymmetry. Recently, it was shown that a modified form of the surface code, XZZX exhibits considerably improved performance under biased noise. In this work, we demonstrate low density parity check can be similarly bias-tailored. We introduce bias-tailored lifted product code construction provides framework expand bias-...