低密度奇偶校验码的压缩感知重构

Compressed sensing reconstruction of LDPC code

针对压缩感知(CS)中由观测噪声引起的信号重建误差问题,提出利用非相关性约束理论作为衡量压缩重建条件的重构误差向量的方法。该方法基于线性分组码中稀疏校验矩阵的零化子特性,建立了以误差向量为目标信号的线性规划问题,实现了低密度奇偶校验(LDPC)码的压缩感知重构。仿真结果表明:在加性高斯白噪声信道和原对偶内点算法下,选取的3种LDPC码均具备较强的信号重构能力,其中Mac Kay随机码的相关性系数较小,因此在信噪比为-1 d B时就可达到100%的误差向量重构成功率。同时表明在满足误比特率要求下,CS-LDPC码可使系统实现低信噪比下的高可靠性通信。

In order to resolve the problem of signal reconstruction error caused by observation noise in Compressed Sensing （CS）, a method is proposed to reconstruct error vectors using the theory of non- correlation constraint as the condition. In this method, a linear programming for error vectors is established based on the annihilator property of sparse check matrix; and compressed sensing reconstruction for Low-Density Parity-Check （LDPC） codes is implemented. Under an additive white Gauss noise channel and primal-dual interior point algorithm, simulations show that three selected （LDPC） codes all satisfy non-correlation constraint condition with high reconstruction ability. Moreover, the correlation coefficient of MacKay random codes is smaller, therefore 100% success rate is obtained in reconstructing error vectors with SNR of -1 dB. The simulation results also show that under the condition of satisfying the requirement of Bit Error Rate （BER） performance, high reliability communication can be achieved with low SNR by the proposed CS-LDPC codes.