Abstract
Many different encoding algorithms for systematic polar codes (SPC) have been introduced since SPC was proposed in 2011. However, the number of the computing units of exclusive OR (XOR) has not been optimized yet. According to an iterative property of the generator matrix and particular lower triangular structure of the matrix, we propose an optimized encoding algorithm (OEA) of SPC that can reduce the number of XOR computing units compared with existing non-recursive algorithms. We also prove that this property of the generator matrix could extend to different code lengths and rates of the polar codes. Through the matrix segmentation and transformation, we obtain a submatrix with all zero elements to save computation resources. The proportion of zero elements in the matrix can reach up to 58.5% from the OEA for SPC when the code length and code rate are 2048 and 0.5, respectively. Furthermore, the proposed OEA is beneficial to hardware implementation compared with the existing recursive algorithms in which signals are transmitted bidirectionally.
Highlights
Polar codes proposed by Arikan [1] can theoretically reach the Shannon limit
According to an iterative property of the generator matrix and particular lower triangular structure of the matrix, we propose an optimized encoding algorithm (OEA) of systematic polar codes (SPC) that can reduce the number of Exclusive Or (XOR) computing units compared with existing non-recursive algorithms
The proposed OEA is beneficial to hardware implementation compared with the existing recursive algorithms in which signals are transmitted bidirectionally
Summary
Polar codes proposed by Arikan [1] can theoretically reach the Shannon limit. It has been widely given attention in the communication field because of its low complexity and good decoding performance. According to an iterative property of the generator matrix and particular lower triangular structure of the matrix, we propose an optimized encoding algorithm (OEA) of SPC that can reduce the number of XOR computing units compared with existing non-recursive algorithms. Through the matrix segmentation and transformation, we obtain a submatrix with all zero elements to save computation resources.
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More From: EURASIP Journal on Wireless Communications and Networking
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