BEC上基于内插算法的多元SC-LDPC码BP译码波速度分析

BP Decoding Waves Velocity Analysis of Non-binary SC-LDPC Code Based on Interpolation Approach on BEC

针对多元空间耦合低密度奇偶校验(Spatially-Coupled Low-Density Parity-Check,SC-LDPC)码在二进制擦除信道(Binary Erasure Channel,BEC)上置信传播(Belief Propagation,BP)译码的译码波速度分析复杂度较高的问题,提出了内插密度演进(Density Evolution,DE)算法。内插DE算法利用一维函数在非耦合DE递归式的不动点间插值密度来近似表示轮廓译码(Decoding Profile,DP),避免了高维耦合DE递归式的迭代,从而降低了计算复杂度。仿真和分析结果表明,在相同的度分布和信道条件下,内插DE算法计算的译码波速度与传统的耦合DE算法计算的译码波速度误差在[0,0.05],特别在信道删除概率为耦合DE算法的BP阈值时,两者测得速度相等;由内插DE算法计算所得的BP阈值与耦合DE算法的BP阈值相等。

In order to reduce the computational complexity in analyzing the decoding wave velocities of non-binary spatially-coupled low-density parity-check(SC-LDPC)codes on binary erasure channel(BEC)under belief propagation(BP)decoding,an interpolated density evolution(DE)approach is proposed.The approach uses one-dimensional functions to interpolate density between some fixed points(FPs)of the uncoupled DE recursion to approximate the decoding profile(DP),which avoids the iteration of high-dimensional DE recursions and reduces the computational complexity.Simulation and analysis results show that the error between the decoding wave velocities calculated by the interpolated DE approach and that calculated by traditional coupled DE approach is between 0 and 0.05,especially when the channel erasure probability is equal to the BP threshold of the coupled DE approach,the velocities calculated by the interpolated DE approach and the coupled DE approach are equal.The BP threshold of the interpolated DE approach is equal to that of coupled DE approach.