A Low Complexity Encoding Algorithm for Systematic Polar Codes

TL;DR

This paper introduces a low-complexity, memory-efficient encoding algorithm for systematic polar codes that also supports parallel processing, outperforming existing methods in efficiency and throughput.

Contribution

It presents a novel encoding algorithm for systematic polar codes that reduces memory and computational complexity while enabling parallel encoding, applicable to both systematic and nonsystematic polar codes.

Findings

Requires only N bits of memory

Uses N/2 * log2 N XOR operations

Supports parallel 2-bit encoding with same complexity

Abstract

Arikan has shown that systematic polar codes (SPC) outperform nonsystematic polar codes (NSPC). However, the performance gain comes at the price of elevated encoding complexity, i.e., compared to NSPC, the available encoding methods for SPC require higher memory and computation. In this letter, we propose an efficient encoding algorithm requiring only $N$ bits of memory and having $\frac{N}{2}\log_2N$ XOR operations. Moreover, the auxiliary variables in the algorithm can share the memory to reduce extra memory requirement. Furthermore, a parallel 2-bit encoding algorithm is also presented to improve the encoding throughput. Remarkably, we show that parallel encoding can be implemented with the same number of XOR operations and memory bits. Finally, the proposed encoding algorithm can be directly used for NSPC with the same complexity.