# Optimized Polar Codes as Forward Error Correction Coding for Digital Video Broadcasting Systems  
[PERSON]  
1 Spectrum Management and Regulatory Affairs Department, The Egyptian Satellite Company (Nilesat), Cairo 12568, Egypt 12 Electronics and Communications Engineering Department, Faculty of Engineering, Ain Shams University, Cairo 11517, Egypt; [EMAIL_ADDRESS]  
[PERSON]  
such systems require flexible medium and short code lengths, such as real-time video communication systems. This obstacle was overcome by constructing polar codes with arbitrary code length through various puncturing strategies, as shown in [4; 5]. In all these strategies, the punctured bits are obtained by removing some of the encoder output bits according to a pre-determined puncturing pattern optimized by one of these strategies. The punctured bits are not sent over the channel, and before decoding process the corresponding Log-Likelihood Ratios (LLRs) for these removed bits are set again according to a pre-defined value in puncturing algorithm. While these methods allow for the construction of arbitrary length polar codes, the wrong selection of puncturing bits location could alter the polarization process of the codes and could decrease decoding error-rate performance [6]. On the other hand, the generation of polar codes using different higher dimensions \(m\times m\) binary kernel matrix has been introduced in [7; 8; 9; 10; 11]. These methods describe the choice of the best kernel matrix with maximum exponent that provides the highest performance. A family of polar codes based on multi-kernel (MK) constructions have been presented in [12; 13], which showed that the channel polarization condition still applies for such MK polar codes. In recent years, the concept and design principles of MK polar codes have become a significant research area [6; 14; 15]. Therefore, flexible code lengths can be obtained using MK construction by applying the Kronecker product for different base kernels matrices with various dimensions. Another concern related to polar codes is their channel-specific nature, which requires optimizing polar codes construction for the given channel [3]. Actually, polar code optimization is about selecting the right indices for the most reliable channels from the synthesized channels. This can be determined by the Bhattacharyya parameter bounds [1]. However, closed-form expressions for the Bhattacharyya parameter bounds of the synthesized channels are usually unavailable for general channels [16]. Moreover, the reliability of the synthesized channels can be acquired by other three popular techniques which are Monte-Carlo estimation approach [1], density evolution (DE) technique [17], and Gaussian approximation (GA) technique [18]. These methods define each synthetic channel as a pure-noise channel to be reserved for a frozen bit or noise-free channel to be reserved for an information bit. However, all these techniques depend on the conditions of the transmission channel, which makes it necessary to construct polar codes separately for each signal to noise ratio (SNR) [19]. This can be solved by modelling the channel with all characteristics and designing the code for the worst operating SNR [20]. In general, the optimized SNR design point is very important to construct polar codes where the construction of polar codes plays a significant role in improving its performance, but the major role is related to the decoding method of polar codes. Over the past decade, decoding of polar codes has gone through some improvement stages. Polar codes decoding started from the simple Successive Cancellation Decoding (SCD) method proposed by [PERSON] [1]. Subsequently, it has been enhanced several times using advanced decoding techniques such as SCL decoding [21]. In SCL, a list of size \(L\) of SCD paths is concurrently generated at each decoding stage to select the best paths. SCL decoding was improved later in [22] to Cyclic Redundancy Check (CRC) Aided SCL (CA-SCL), where CRC detector selects the correct codewords from the list.