On fuzzy syndrome hashing with LDPC coding

Soft Syndrome Decoding of Quantum LDPC Codes for Joint Correction of Data and Syndrome Errors

Quantum errors are primarily detected and corrected using the measurement of syndrome information which itself is an unreliable step in practical error correction implementations. Typically, such faulty or noisy syndrome measurements are modeled as a binary measurement outcome flipped with some probability. However, the measured syndrome is in fact a discretized value of the continuous voltage or current values obtained in the physical implementation of the syndrome extraction. In this paper, we use this "soft" or analog information without the conventional discretization step to benefit the i…

Design and Analysis of Time-Invariant SC-LDPC Convolutional Codes With Small Constraint Length

In this paper, we deal with time-invariant spatially coupled low-density parity-check convolutional codes (SC-LDPC-CCs). Classic design approaches usually start from quasi-cyclic low-density parity-check (QC-LDPC) block codes and exploit suitable unwrapping procedures to obtain SC-LDPC-CCs. We show that the direct design of the SC-LDPC-CCs syndrome former matrix or, equivalently, the symbolic parity-check matrix, leads to codes with smaller syndrome former constraint lengths with respect to the best solutions available in the literature. We provide theoretical lower bounds on the syndrome form…

Interactive Encoding and Decoding Based on Binary LDPC Codes with Syndrome Accumulation

Interactive encoding and decoding based on binary low-density parity-check codes with syndrome accumulation (SA-LDPC-IED) is proposed and investigated. Assume that the source alphabet is $\mathbf{GF}(2)$, and the side information alphabet is finite. It is first demonstrated how to convert any classical universal lossless code $\mathcal{C}_n$ (with block length $n$ and side information available to both the encoder and decoder) into a universal SA-LDPC-IED scheme. It is then shown that with the word error probability approaching 0 sub-exponentially with $n$, the compression rate (including both…

Generalized reliability-based syndrome decoding for LDPC codes

Aiming at bridging the gap between the maximum likelihood decoding (MLD) and the suboptimal iterative decodings for short or medium length LDPC codes, we present a generalized ordered statistic decoding (OSD) in the form of syndrome decoding, to cascade with the belief propagation (BP) or enhanced min-sum decoding. The OSD is invoked only when the decoding failures are obtained for the preceded iterative decoding method. With respect to the existing OSD which is based on the accumulated log-likelihood ratio (LLR) metric, we extend the accumulative metric to the situation where the BP decoding …

HARS：基于初始综合征条件参数映射与局部可靠性加权的LDPC比特翻转译码

HARS: LDPC Bit-Flipping Decoding With Initial-Syndrome-Conditioned Parameter Mapping and Local-Reliability Weighting

HARS通过结合局部可靠性和初始综合征参数映射，实现LDPC比特翻转译码，显著降低BER和迭代次数，并在FPGA上达到高吞吐量。

综合征自适应增益控制用于量子低密度奇偶校验码的Min-Sum解码

Syndrome Adaptive Gain Control for Min-Sum Decoding of Quantum LDPC Codes

本文提出一种自适应增益Min-Sum解码器，用于量子低密度奇偶校验码，通过动态调整消息增益提升解码性能，无需预先优化。