Discrete BP Polar Decoder Using Information Bottleneck Method

Polar code is one of the channel codes and is used in the 5th generation of mobile communication system (5G). This encoding scheme is based on the operation of channel polarization, and it is possible to achieve the capacity of arbitrary binary-input symmetric discrete memoryless channels. Compared with Turbo codes and LDPC (Low-Density Parity-Check) codes, the implementation of the encoder and decoder is easier. BP (Belief Propagation) decoding, one of the decoding methods of the polar codes, can be performed at high speed because it can decode in parallel. However, the disadvantages of the BP decoding are the hardware and computational complexities. The technique of quantization can be used to reduce complexities of hardware and calculation. One of the quantization methods is the information bottleneck method, which allows an observation variable to compressed one while trying to preserve the mutual information shared with a relevant variable. As a novel approach, the information bottleneck method is used in the design of quantizers for the BP decoding of LDPC codes. In this paper, we propose a discrete BP polar decoder that can use only unsigned integers in the decoding process by using the information bottleneck method. Thus, we can replace complex calculations of BP decoding with simple lookup tables. We also investigate the minimum bit width for quantization with negligible degradation and the suboptimal
$E_{b}/N_{0}$
for designing lookup tables, where
$E_{b}$
and
$N_{0}$
denote energy per bit and noise power density, respectively. The simulation results show that the proposed method can achieve almost the same error correcting capability compared with the BP decoding without compression in the range of low
$E_{b}/N_{0}$
. Besides, we show that the proposed decoder can compress both channel outputs and BP messages with small loss compared with the uniform quantization decoder.