Technologies Research Of LDPC Codes And Polar Codes

Nowadays,the development of wireless communication systems is getting faster and faster,and more advanced error correction coding techniques are needed to improve the reliability of the transmission process.Low-density parity-check codes and polar codes are the encoding schemes of data channel and control channel respectively adopted by the International Mobile Telecommunications Standardization Organization 3GPP in the 5G Enhanced Mobile Broadband（eMBB）channel coding scheme.LDPC codes are block error correction codes that have the ability to approximate the Shannon limit.Because of the superior performance,LDPC codes were adopted by major communications standards,including WIMAX（Also known as 802.16）（Worldwide Interoperability for Microwave Access）and DTMB（Digital Television Terrestrial Multimedia）and so on.Since the polar codes were first proposed by professor Erdal Arikan in 2008,they have attracted extensive attention and research.Polar codes were the only error correcting codes that have been proved by theory can reach the Shannon limit,what's more,they also have the linear complexity which make it practical.First of all,this paper studies and analyzes the common decoding algorithms of LDPC codes,analyzes the performance of each decoding algorithm of LDPC codes and their advantages and disadvantages.Secondly,this paper studies and analyzes the theory of DE（Density Evolution）,and on the basis of this,combined with BP（Belief Propagation）algorithm and Min Sum（MS）,this paper proposes an algorithm named DE-based Offset Min Sum（DOMS）which is an improved Offset Min Sum（OMS）algorithm of LDPC codes.This algorithm uses the density evolution theory to calculate check nodes to variable nodes（C2V）probability mass function（PMF）of the BP algorithm,the MS algorithm and the Offset Min Sum（OMS）and calculates offset factors₈)based on this.The simulation results show that the improved algorithm proposed in this paper has a gain of about 0.2dB compared with the classical OMS decoding performance.In addition,compared with the LMMSE（Linear Minimum Mean Square Error）Min Sum algorithm,which is very close to the BP algorithm decoding performance proposed in the related literatures,the proposed algorithm can achieve a similar decoding performance while saving about 28.29%of logic elements and 34.33%of storage.Finally,this paper studies the concatenation system based on LDPC codes and polar codes.Aiming at the LDPC code's disadvantages of higher encoding complexity,large hardware resources and error floor,a practical-effective concatenation structure was proposed by concatenating with polar codes.LDPC codes for the inner code,and polar code for the outer code.Compared with LDPC codes under the WIMAX standard,concatenated codes can save about 0.15dB signal-to-noise ratio when the Bit Error Rate was required to reach 10^-3.The frame error rate at 3dB signal-to-noise ratio can have nearly two orders of magnitude performance improved.