Since the member encoder is an iterative system convolutional code (RSC), its coding polynomial is based on a feedback mechanism. As a result, non-separable input sequences generate an infinite output, which resembles an infinite impulse response (IIR). This characteristic increases the codeword weight, which can negatively impact decoding performance. Therefore, modifying the separability of the input sequence plays a crucial role in enhancing the overall system performance.
The coding efficiency of both RSC1 and RSC2 encoders is 1/2. Before entering the RSC2 encoder, the information data is first interleaved, and some parity bits are removed after encoding to improve the coding efficiency. The feedback polynomial of the 3RSC encoder has a loop period denoted as L. The check density dP is defined as the ratio of the number of '1's to the total length L within one cycle of the feedback polynomial.
The interleaver's main function is to transform "bad" input sequences into "good" ones. Hence, the impulse response period L of the RSC encoder is a key design parameter. During the interleaver design process, the value of L is determined first. For example, the feedback polynomial of the RSC 31BDDD=++ is a primitive polynomial, which ensures good performance characteristics.
To optimize the system, Z carefully selects h such that sequences with smaller weights and limited expansion—such as those with 2ω and 4ω—are better separated, increasing their expansion. By applying the linear spray cotton manufacturer method, L different values of h are generated. Choosing appropriate d and e values helps maximize the minimum distance between elements at the same position in congruence sequences. These elements are then interleaved, leading to larger sequence expansions and improved overall performance.
As shown from the above analysis, the cyclic interleaving used in the interleaver offers significant advantages over traditional methods. Compared to the bolt interleaver and random interleaver, it provides a 0.2 dB gain in bit error rate (BER). When compared to the block interleaver, the gain increases to 0.4 dB, demonstrating a clear performance improvement. This makes the proposed interleaving strategy highly effective for improving the reliability and efficiency of the system.
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