高阶量纠错码理论限及软判决编译码算法

Theory performance limit and soft-decision based encoding and decoding algorithm of high order quantity error correction codes

基于tent混沌映射的高阶量纠错码可以实现对图像的线性纠错,解决了压缩图像峰值信噪比(peak signal-to-noise ratio,PSNR)存在的"门限效应"问题。通过对基于tent混沌映射的纠错码的图像PSNR理论限的分析,得出符号位的准确估计是提高码字性能的关键。传统的基于符号位硬判决的编译码方法难以实现对符号位的有效保护。基于此,借鉴低密度奇偶校验(low density parity check,LDPC)码的软判决编译码方法,提出一种基于符号位软判决译码的高阶量纠错码。仿真结果表明:基于符号位软判决译码的高阶量纠错码的图像PSNR不断逼近理论限;与硬判决高阶量纠错码相比,在编译码复杂度相当的情况下(符号位初始化概率通过查表得到),图像PSNR有2dB的增益。

The traditional high order quantity error correction codes, based on the tent chaotic map, have the feature of linear error correction to image. And the ＂threshold effect＂ of compressed image peak signal-tonoise ratio （PSNR） can be resolved. And then the elegant feature and theory image PSNR limit of the error correction codes, based on the tent map, are analyzed. We can get that the accurate estimation of sign bit is the key to improving performance. However, the traditional hard-decision decoding of sign bit becomes the bottleneck to restrict the improvement of performance. That is because the sign bit can not be protected effectively by the traditional high order quantity codes. Based on this, the high order quantity codes, based on soft-decision decoding of sign bit, are proposed. In addition, combined with low density parity check （LDPC） codes, the sign bit can be protected effectively with the soft decision decoding method. Finally, the simulation results show that the image PSNR can approach the theory limit using the proposed high order quantity codes. And compared with the traditional high order quantity codes, the image PSNR can get the gain of 2 dB with the almost same encoding and decoding complexity, when the initial probability of sign bit is obtained by looking up tables.