Since the member encoder is an iterative system convolutional code (RSC), it uses a feedback polynomial as its coding polynomial. This results in non-separable sequences that produce infinite outputs, which are equivalent to infinite impulse responses, thereby increasing the codeword weight. As a result, altering the separability of the input sequence plays a crucial role in enhancing the overall performance of the system.
The coding efficiency of both RSC1 and RSC2 encoders is 1/2. Before entering the RSC2 encoder, the information data is interleaved by the interleaver, and some parity bits are removed after encoding, which helps improve the coding efficiency. The loop period defining the feedback polynomial of the 3RSC encoder is denoted as L, while the check density dP represents the ratio of 1s to the total length L in one cycle of the feedback polynomial.
The interleaver's main purpose is to transform these "bad" input sequences into "good" ones. Therefore, the impulse response period L of the RSC encoder is a critical parameter. During the design process of the interleaver, the value of L is determined first. For example, the feedback polynomial of the RSC 31BDDD=++ is a primitive polynomial, ensuring good spreading properties.
Z carefully selects h such that sequences with smaller weights and expansions at 2ω= and 4ω= are better separated, leading to increased expansion. By using the linear spray cotton manufacturer method, L different h values are obtained. Choosing appropriate d and e can maximize the minimum distance between elements in the same position of the congruence sequence. When these elements from L congruence sequences are interleaved, they become more spread out, thus increasing the sequence's expansion.
As shown in the above analysis, the cyclic interleaving used in the interleaver, compared to the block interleaver, transforms separable sequences of weights 3, 4, 5, and 6 into non-separable ones. This leads to a 0.2 dB gain in bit error rate compared to the block and random interleavers, and a 0.4 dB improvement over the block interleaver, demonstrating a significant performance advantage.
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