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| Searching the Optimal Puncture Matrix for Rate Compatible Punctured Turbo (RCPT) Codes with Density Evolution |
| Lü Shu-juan; Wei Guo; Zhu Jin-kang |
| PCN&SS Lab, University of Science and Technology of China, Hefei 230027, China |
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Abstract A new algorithm for searching the optimal puncture matrices of the rate compatible punctured Turbo(RCPT) codes is proposed. The algorithm is based on density evolution and its main goal is to analyze the thresholds for different puncture matrices. The thresholds are calculated using Gaussian approximation and simulation. Compared to a conventional distance spectrum approach, this new approach has two advantages. The first advantage is that the new algorithm is independent of the interleaver. The second is that when the Turbo code is very long, the complexity of the calculation will not increase too much for the proposed approach. In AWGN channels, when the code is long, the examples shows that the optimal puncture matrices are the same for both approaches while the proposed approach has reduced computational complexity. This paper also analyzes the puncture matrices of the code used in 3GPP and provides the optimal matrices and thresholds. The result shows that the rate matching algorithm given in 3GPP corresponds to some RCPT matrixes when using puncturing and these matrixes are the same as those optimal matrices given in this paper for certain rates.
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Received: 08 May 2005
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2007, Vol. 29 
