Fast Calculation of Polar Code Bits and Frozen-Bit Locations

Yıl 2021, Cilt: 18 Sayı: 2, 125 - 132, 01.11.2021

Fatih Genc Orhan Gazi

Öz

In this paper, we show that encoding operation for the polar codes can be achieved without the employment of the generator matrix, and all the polar code bits can be generated at the same time using a number of tree-encoding structures running in parallel. Since encoding matrix is not used in the implementation of the polar encoders in digital electronic devices, hardware space is saved, and low complexity hardware applications are achieved. Besides, we also proposed a method for the calculation of split channel parameters, such as Bhattacharyya bounds or average-bit-error probabilities of the transmitted bits using a tree-based structure. Moreover, the proposed structure enables to calculate the probability of bit-error values of all the transmitted bits at the same time in a parallel manner and decide the locations of data and frozen bits very rapidly.

Anahtar Kelimeler

Polar codes, encoding algorithm, generator matrix transformation, tree structure, FPGA.

Kaynakça

• [1] O. Gazi, Polar Codes: A Non-Trivial Approach to Channel Coding, Springer Verlag, 2019.
• [2] I. Tal and A. Vardy, “ List decoding of polar codes,” IEEE International Symposium on Information Theory - Proceedings, pp. 15, 2011.
• [3] K. Niu and K. Chen, “Stack decoding of polar codes,” Electronics Letters, vol. 48, no. 12, pp. 695697, 2012.
• [4] K. Chen, K. Niu, and J. Lin, “Improved successive cancellation decoding of polar codes,” IEEE Transactions on Communications, vol. 61, no. 8, pp. 31003107, 2013.
• [5] B. Li, H. Shen, and D. Tse, “ An adaptive successive cancellation list decoder for polar codes with cyclic redundancy check,” IEEE Communications Letters, vol. 16, no. 12, 2012.
• [6] E. Arikan, “ Channel polarization: A method for constructing capacity achieving codes for symmetric binary-input memoryless channels,” IEEE Transactions on Information Theory, vol. 55, no. 7, pp. 30513073, 2009.
• [7] A. Çağrı Arlı, O. Gazi, “ Noise-aided Belief Propagation List Decoding of Polar Codes,” IEEE Communications Letters, pp: 1285-288, 2019.
• [8] K. Niu and K. Chen, “ CRC-aided decoding of polar codes,” IEEE Communications Letters, vol. 16, no. 10, pp. 16681671, 2012.
• [9] A. A. Andi, O. Gazi, “ Fast Decoding of Polar Codes Using Tree Structure,” IET Communications, vol. 13, no. 14, pp. 2063-2068, 2019.