Efficient Implementations Of Belief Propagation Decoder For Polar Codes

Channel coding is an important part of modern communication systems and it improves the reliability of digital signals during transmission by adding redundant information.Since Shannon's information theory was proposed,numerous researchers have been working hard to explored the channel coding that could achieve the Shannon capacity.In2008,Professor Ar(?)kan proposed the encoding and decoding method of polar code,which was proved that this new coding method can achieve the Shannon capacity for binary discrete memoryless channels.However,faced with the performance requirements raised by applications that come along with next generation communications such as 5G wireless and Internet of Things(Io T),polar decoder has to increase either its list size L(for SCL decoding)or iteration number I(for BP decoding).This makes balancing between decoding performance and hardware complexity an inevitable concern for all designers.Firstly,we introduced the approximate computing technique into the designing of BP decoders for polar code.In practical applications,it is not always nessasary to require a 100% calculation accuracy for a computing system.Approximate computing is a technique that exchanges a large amount of hardware resource consumption with an acceptable reduction in calculation accuracy.Approximate computing technology can greatly reduce the hardware complexity of the computing system Especially in some errorresilient systems such as image processing,handwritten recognition,and neuromorphic systems.In addition,decoders of forward error correction(FEC)codes can be viewed as an error-resilient system since they work with noisy channel inputs.Benefit from approximate computing scheme,we can set different approximation parameters according to the specific scenario and users' requirements and balance the decoding performance and the complexity of the BP decoders.On the other hand,stochastic Computing,which uses random bit sequences to perform operations,is a lower-cost alternative to traditional binary computing circuits.It is known for its super high hardware efficiency and error tolerance.Stochastic computing is proposed to use lowest hardware cost to implement logic operations.However,its promotion and application value has been limited because of its low computational accuracy.Based on this,this paper combined the BP decoding algorithm of polar code and the stochastic computing schemeand proposed a stochastic BP decoding algorithm for polar code to reduce the hardware cost of the traditional BP decoder for polar codes.We also give the corresponding optimization strategy to ensure the decoding performance of the proposed stochastic BP decoder.Firstly,we analyze the existing BP decoding algorithm of polar codes based on traditional binary calculation.We convert the channel information stored in the form of likelihood ratio(LR)from real number field to probability realm and use random sequence to represent the value.Next,we modify the BP decoding algorithm based on traditional binary computing from three aspects: the initialization of channel information,the update formula of the computing node in the BP algorithm,and the decision rule based on stochastic calculation.And we also give the corresponding circuit design for the proposed stochastic decoder for polar code.Then,starting from the accuracy of the stochastic calculation itself,we analyzed the factors that could affect the accuracy of the stochastic calculation and the decoding performance of the proposed stochastic decoder for polar code based on the definition of stochastic computing correlation(SCC),we explain how Bit Aggregation phenomenon leads to the change of SCC in BP decoding process,which consequently results in the loss of decoding performance.The factors are as follows: the fluctuation of the random bit sequence,the accuracy of the random bit sequence,and the correlation between the random bit sequences.Afterwards,according to the three factors that affect the decoding performance of the proposed stochastic decoder for polar code,we give the corresponding optimization strategies,including: adjusting the length of the random bit sequence,re-randomizing the part of the random bit sequences in stage-wise manner and scaling the channel information.And we also give the corresponding circuit module design.The simulation based on matlab shows that the decoding performance of the stochastic decoder using the above optimization module can reach the performance level of the traditional BP decoder.Meanwhile,the hardware synthesis results show that,compared with the existing random decoder,the average decoding delay of the proposed stochastic decoder is reduced by more than 90%.Compared to the traditional BP decoder,the circuit area of the decoder in this paper is reduced by 84.2%,which has the highest hardware efficiency.