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Performance Analysis of Polar Codes
Published in Durgesh Kumar Mishra, Nilanjan Dey, Bharat Singh Deora, Amit Joshi, ICT for Competitive Strategies, 2020
M. Valarmathi Saila, Shanthi Prince
Encoding in polar codes is done by the splitting of the total codeword of length N into message bits and frozen bits (least reliable or worst channels). The message of length K bits should be always less than or equal to the codeword length N (K<=N). A vector u of length N bits is formed with N-K as the frozen positions and the remaining positions as the message positions. The frozen positions are always set to zero. Encoding is performed in a bottom to top fashion, that is, the bits at the bottom are evaluated first and then we move towards the top. Figure 35.2 shows the process of encoding for N=4 codeword.
Information Theory
Published in Jerry D. Gibson, Mobile Communications Handbook, 2017
Emmanuel Abbe, Bixio Rimoldi, Rüdiger Urbanke
Invented in 2008 by Erdal Arikan (see Arikan 2009), polar codes constitute a new family of linear codes. The original construction of polar codes relies on a different intuition than the construction of LDPC codes. Rather than focusing on the parity-check matrix, a probabilistic phenomenon called “channel polarization” is used to guide the code construction. We next explain this phenomenon in the source setting, which is also called the “source polarization.”
Overview of the challenges and solutions for 5G channel coding schemes
Published in Journal of Information and Telecommunication, 2021
Madhavsingh Indoonundon, Tulsi Pawan Fowdur
Arikan invented a class of linear block codes called Polar codes (2009). Arikan and Telatar (2008) derived equation (3) to calculate the probability of error for polar codes in a binary memoryless symmetric channel (BMSC):