Performance of Gaussian Belief Propagation Decoding For Polar Codes in The AWGN Channel

Abstract

Since Arikan introduced in 2008, Polar Code has become one of the hot topics in channel code field. The best advantages of polar code are a low complexity algorithm for encoding as well as decoding and capacity achievement in binary input discrete memoryless channel (B-DMC). However, the decoding technique in Polar Codes is the controversial topic, in which the Successive Cancellation (SC) decoder in the Arikans paper only provided for the BEC channel. Nowadays, a lot of researchers are discussing about decoding in Polar Code to adapt for others channel, especially for continuous channel such as AWGN channel. In this case, Belief Propagation decoder from Low-Density Parity Check code (LDPC) code and List Success Cancellation decoder are considered as the potential decoders which provide the higher performance of Bit Error Rate (BER) not only BEC channel, also AWGN channel. In other ways, some authors take great effort to expand the block-length for Polar Codes from to with by figure out the characteristic of generator matrices of polar codes (from the transform matrices). From these properties, we apply a generator matrix for block-length , which are used as transform matrices for Polar code systems. There exist more than ten candidates of such size kernel matrix. In previous researches, the authors only apply SC decoder for polar code block length in AWGN channel. However, not all of generator matrices in polar code block length achieved the good performance with SC Decoder. In this study, I propose the Gaussian Belief Propagation Decoder which owns some advantages adapting for polar codes of block length . This work improves the performance of BER for any cases which obtained the limited results when using SC decoder. In this thesis, I present the Gaussian Belief Propagation Decoder in Polar Code with the comparison to Belief Propagation decoder and SC decoder. In addition, the results will be the BER performance of Gaussian BP decoder and the capacity of system for each of generator matrices with block length following varies of code rate and SNR.

Key words: Channel coding, Polar Codes, Gaussian Belief Propagation decoder, Belief Propagation decoder.