Discrete Polar Decoder using Information Bottleneck Method

Abstract

Polar codes are attracting much attention and being used for control channels of the 5th generation of mobile communication system (5G). As a feature, it is easier to implement encoder and decoder than Turbo codes and LDPC (Low Density Parity Check) codes. One of the decoding methods of polar codes is BP (Belief Propagation) decoding, which can decode in parallel, so that decoding can be performed at high speed. However, due to hardware limitation, calculations on the decoder get very complicated. This issue can be solved by using the information bottleneck method. This method compresses an observation variable to a quantized one while attempting to preserve the mutual information shared with a relevant random variable. In the conventional research, the information bottleneck method is applied to the BP decoding of the LDPC codes. In this paper, the information bottleneck method is used for the BP decoding of polar codes. The BP decoding of polar codes is distinct from that of LDPC codes. It has several types of the messages, and each time a message is updated, the decoding becomes more complex. By using the information bottleneck method, the decoder can compress the channel outputs and the messages of BP into unsigned integers while preventing degradation of the error correcting performance. Thus, we can reduce the complexity of calculation in the decoding process and easily implement the decoder. This paper also investigates the minimum bit width for quantization with negligible degradation and the suboptimal E <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">b</sub> /N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> for designing the lookup tables. These lookup tables are used for updating the messages. The simulation results show that the error correcting capability of the discrete polar decoders of the proposed method is negligibly degraded compared to the BP decoding without compression.