Understanding turbo codes: A signal processing study

Journal of Information and Intelligence Pub Date : 2024-01-01 DOI:10.1016/j.jiixd.2023.10.003

Xiang-Gen Xia

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Abstract

In this paper, we study turbo codes from the digital signal processing point of view by defining turbo codes over the complex field. It is known that iterative decoding and interleaving between concatenated parallel codes are two key elements that make turbo codes perform significantly better than the conventional error control codes. This is analytically illustrated in this paper. We show that the decoded noise mean power in the iterative decoding decreases when the number of iterations increases, as long as the interleaving decorrelates the noise after each iterative decoding step. An analytic decreasing rate and the limit of the decoded noise mean power are given. The limit of the decoded noise mean power of the iterative decoding of a turbo code with two parallel codes with their rates less than 1/2 is one third of the noise power before the decoding, which can not be achieved by any non-turbo codes with the same rate. From this study, the role of designing a good interleaver can also be clearly seen.

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了解涡轮编码：信号处理研究

本文从数字信号处理的角度出发，通过定义复数域上的涡轮编码来研究涡轮编码。众所周知，迭代解码和并行编码之间的交错是使涡轮编码的性能明显优于传统误差控制编码的两个关键因素。本文通过分析说明了这一点。我们证明，只要交织在每个迭代解码步骤后对噪声进行去相关处理，迭代解码中的解码噪声平均功率就会随着迭代次数的增加而减小。给出了解析递减率和解码噪声平均功率的极限。用两个速率小于 1/2 的并行编码对一个涡轮编码进行迭代解码的解码噪声平均功率的极限是解码前噪声功率的三分之一，这是任何具有相同速率的非涡轮编码都无法达到的。从这项研究中，我们也可以清楚地看到设计一个好的交织器的作用。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Journal of Information and Intelligence

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