# CRCSI: A Generic Block Interleaver for the Next Generation Terrestrial Broadcast Systems
## 1 Introduction  
In order to improve the reliability of wireless transmission, it is necessary to introduce interleaving technologies into the system, where the transmitted bit or symbol sequence is reordered according to a specific interleaving rule to repair the channel damage caused by burst errors [1]. Bit interleaving can break the inherent correlation in the input bit sequence through certain permutation rules, and the original bit sequence is wisely reordered, enhancing the ability to resist burst errors [2]. Bit interleaving is widely used in the design of Forward Error Correction (FEC) codes such as Turbo code [3] and LDPC code. There are many bit interleavers studied in the literature. Among them, the random interleaver [4] uses a string of randomly generated permutation indexes to permutate the input data, and then de-interleaves it with the knowledge of permutation patterns. Although this method is able to achieve good performance, it is time-consuming and requires a lot of storage space to store the large random interleaver. In order to reduce the resources consumed by the interleaving, [PERSON] et al. studied the use of a Quadratic Polynomial Permutation (QPP) in LTE to produce a regular interleaver with the statistical property of random interleavers [5]. Considering that the length of burst error is random, [PERSON] et al. [6] proposed the Dithered Golden Interleaver (DGI) which achieves a good spreading property by adding a randomcomponent to golden interleavers. However, the golden section method does not apply to all lengths [7]. To resolve this issue, based on the regular permutation method, Dithered Relative Prime (DRP) interleavers and Almost Regular Permutation (ARP) interleavers [4; 7] were also developed, which can achieve excellent interleaving performance with the same Hamming distance. The above-mentioned bit interleaving methods perform well over memoryless channels, especially when errors are randomly distributed and statistically distributed. However, when transmitted over impulse noise and/or selected fading channels, the error rate performance of the bit sequence will be greatly deteriorated due to the limited error correction capability of FEC. Therefore, it is of great importance to introduce the channel interleaver [8]. By taking advantage of time and frequency diversities of the encountered channel, the codewords belonging to the same frame are distributed as far apart as possible. In order to combat the impulse noise and the time-frequency selective fading, the block interleaver suitable for processing time-frequency resource mapping has become the predominant choice of researchers in designing channel interleavers. In the Digital Video Broadcasting Terrestrial (DVB-T2) standards [9], the classic row-column interleaver (RCI) is introduced, which has the simple and practical characteristics of writing in columns and reading row-wisely. In the Advanced Television Systems Committee (ATSC) 3.0 [10] system, a twisted block interleaver (TBI) is used, which rotates each row to the left and reads it out column by column. This method can achieve a good time diversity. However, since the row or column reading interval of the above two block interleavers is fixed at 1, the transmitted data cannot fully obtain the time and frequency diversity in a channel with uneven time-frequency selectivity, i.e., clustering errors. Therefore, how to maximize the time and frequency diversity gain is worth studying. To achieve this, [PERSON] [11] proposes a two-dimensional interleaver with Latin rectangles based on sphere-packing model [12; 13], and then extends the design to correct arbitrary shaped cluster errors in [14; 15]. Nevertheless, these schemes can only maximize the time diversity gain, and only consider data blocks with a large number of columns. Therefore, it is not suitable for multi-carrier terrestrial broadcast transmission with more rows [16]. In this paper, a generic block interleaver jointly considering the time and frequency diversity in the fading channels is developed.