Simplified Successive Cancellation Decoding of Polar Codes With Medium-Dimensional Binary Kernels

Abstract

A method for efficiently successive cancellation (SC) decoding of polar codes with high-dimensional linear binary kernels (HDLBK) is presented and analyzed. We devise a lexpressions method which can obtain simplified recursive formulas of SC decoder in likelihood ratio form for arbitrary linear binary kernels to reduce the complexity of corresponding SC decoder. By considering the bit-channel transition probabilities W (⋅) G (⋅ 0) and W (⋅) G (⋅ 1) separately, a W -expressions method is proposed to further reduce the complexity of HDLBK based SC decoder. For a m × m binary kernel, the complexity of straightforward SC decoder is O(2 m N log N ). With W -expressions, we reduce the complexity of straightforward SC decoder to O(m 2 N log N ) when m ≤ 16. Simulation results show that 16×16 kernel polar codes offer significant advantages in terms of error performances compared with 2 × 2 kernel polar codes under SC and list SC decoders.

Minimum-Distance Based Construction of Multi-Kernel Polar Codes

“…The boxplus operator for two LLRs a and b may be evaluated exactly as a⊞b = 2 tanh −1 tanh a 2 ·tanh b 2 or approximately as a ⊞ b ≈ sgn a · sgn b · min{|a|, |b|}; the extension to multiple LLRs is as usual. For other kernels similar LLR update equations can be derived [14]. In the next section, we will show that the presented kernels T 3 and T 5 permit to construct multi-kernel polar codes with good minimum distance.…”

Large Kernel Polar Codes with efficient Window Decoding

“…(3) The complexity of this decoder for a polarization kernel K of dimension l × l is O(2 l N log l N ). Methods for marginally reducing this complexity were proposed in [10] and [11], however, even for small l this is still not practical.…”

Hash-Polar Codes With Application to 5G

“…The capacity can be achieved by employing the noiseless bit-channels for data transmission. Since the error-correcting performance under the simple SC decoding for polar codes with finite code length is inferior to other modern codes such as low-density parity-check (LDPC) codes and Turbo codes, successive cancellation list (SCL) decoding was proposed in 2011 [2]- [5], where L paths were kept at each decoding tree level to select the most likely estimation. In [6], an adaptive SCL decoding algorithm was provided.…”