Design and analysis of nonbinary LDPC codes for arbitrary discrete-memoryless channels
Design and analysis of nonbinary LDPC codes for arbitrary discrete-memoryless channels
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DOI：
10.1109/tit.2005.862080
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发表时间：
2006-02-01
影响因子：
2.5
通讯作者：
Burshtein, D
中科院分区：
文献类型：
--
作者：
Bennatan, A;Burshtein, D
我们提出了一个分析下的陪集低密度奇偶校验（LDPC）码在GF（q），设计用于任意离散无记忆信道（特别是非二进制和非对称信道）的迭代解码。我们使用随机陪集分析产生的效果，类似于输出对称与二进制通道。我们表明，随机选择的GF（q）奇偶校验矩阵的非零元素诱导的密度的解码器消息，这简化了他们的分析和近似的perinutation-invariance属性。通过对二进制LDPC码的分析，我们概括了LDPC码的对称性和稳定性等性质。我们表明，在高斯近似下，整个q - 1维分布的矢量消息是由一个单一的标量参数（如二进制LDPC消息的分布）。我们应用此属性来开发外部信息传输（EXIT）图表为我们的代码。我们使用适当设计的信号星座来获得实质性的整形增益。仿真结果表明，我们的代码优于多级码在短块长度。我们还提出了加性白色高斯噪声（AWGN）信道的仿真结果，包括在不受限制的香农极限（即，不限于任何信号星座）。
We present an analysis under the iterative decoding of coset low-density parity-check (LDPC) codes over GF(q), designed for use over arbitrary discrete-memoryless channels (particularly nonbinary and asymmetric channels). We use a random-coset analysis to produce an effect that is similar to output symmetry with binary channels. We show that the random selection of the nonzero elements of the GF(q) parity-check matrix induces a perinutation-invariance property on the densities of the decoder messages, which simplifies their analysis and approximation. We generalize several properties, including symmetry and stability from the analysis of binary LDPC codes. We show that under a Gaussian approximation, the entire q - 1-dimensional distribution of the vector messages is described by a single scalar parameter (like the distributions of binary LDPC messages). We apply this property to develop extrinsic information transfer (EXIT) charts for our codes. We use appropriately designed signal constellations to obtain substantial shaping gains. Simulation results indicate that our codes outperform multilevel codes at short block lengths. We also present simulation results for the additive white Gaussian noise (AWGN) channel, including results within 0.56 dB of the unrestricted Shannon limit (i.e., not restricted to any signal constellation) at a spectral efficiency of 6 bits/s/Hz.