Turbo译码算法的分岔与控制

Turbo码在信道编码中通过迭代译码的方式可以较好的逼近香农限.本文以其译码算法中的迭代次数作为时间轴，译码输出作为状态变量，信噪比SNR及信息比特数N作为系统参数建立动力学模型，研究Turbo译码输出与迭代次数之间的关系.通过大量计算机仿真和理论分析发现随着信噪比SNR由小到大，译码算法先后经历了不确定不动点、奇异区和清晰不动点三个阶段，其中在由不确定不动点过渡到奇异区时发生了分岔现象.通过改变信息比特数N的方法得到了离散时间动力学中的切分岔、倍周期分岔和Neimark-Sacker分岔 .在奇异区内观察到倍周期、准周期、周期三、混沌等不同的相空间轨迹.奇异区的出现给Turbo码在低信噪比下的应用带来了一定困难，本文通过延迟反馈控制的方法将相空间轨道稳定到不动点上，仿真结果表明，本算法可以使Turbo码在低信噪比奇异区内获得0.1—0.3 dB的增益. 关键词： Turbo译码算法 动力学 分岔 混沌 延迟反馈控制法

Bifurcation analysis and control in Turbo decoding algorithm

Turbo Codes can approach the Shannon limit very closely with the help of its special iterative decoding algorithm. This paper establishes a nonlinear dynamic system to analyze the relationship between Turbo decoding output and the number of iterations. Here, the number of iterations is taken as the time axis, decoding output as the state variable, SNR and information bits N as system parameters. It is shown that with SNR increasing, the decoding algorithm undergoes three stages, namely the indecisive fix-point, singular region and unequivocal fix-point. Bifurcations occur during the transformation from the indecisive fix-point to the singular region. It is first proposed that fold, period doubling and Neimark-Sacker bifurcation all have the possibility to occur, depending on the value of N. In the singular region, phase trajectories may appear as period-two, periodthree, quasiperiod and chaos. This paper first observed and confirmed the existence of period-three and chaos. Singular region deteriorates the performance of Turbo codes under low SNR. This paper proposes a time-delay feedback control method to stablize the fix-point. Simulation results show that this method achieves 0.1-0.3 dB improvement for Turbo codes under low SNR condition.