Joint Channel Estimation And Decoding Of Polar Codes For Channels With Memory

The polar codes can be theoretically proved to reach the Shannon limit.Once proposed as a new channel coding technology,the polar codes quickly find its application in 5G,and can be predicted to be one of the potential coding schemes for 6G.However,A lot of the works on polar codes involve only memoryless channels,while in practice,channels with memory widely exist in communication and strage systems.Moreover,most decoding algorithms of polar codes typically require the perfect knowledge of channel parameter or channel state in advance,which is too idea an assumption in practice,especially for channels with memory.Aiming at improving the decoding performance of polar codes in actual usage scenarios and meet higher transmission requirements in 6G,this paper mainly studies the joint channel state estimation and decoding of polar codes when the channel parameters are unknown.We consider a special kind of finite-state channels different from Inter Symbol Interference(ISI)channels,in which the parameter of additive channel noise is Markov-varying.Specifically,we study a generalized Gilbert-Elliott(GE)channel model,which assumes that the channel switches between a finite number of states.The generalized GE channel in this paper is actully a Binary Symmetric Channel(BSC)or an Additive White Gaussian Noise(AWGN)with timevarying crossover probability or noise variance determined by finite-state Markov process.On the platform of Soft Cancellation(SCAN),this paper proposes three adaptive algorithms.The main innovation of this paper is as follows:(1)The SCAN decoding algorithm in the Likelihood Ratio field(LR-field)is extended to be implemented in the Likelihood field(L-field)and the Log-Likelihood Ratio field(LLRfield).Then the performances of SCAN algorithm are analyzed and compared in three different fields.(2)The joint channel estimation and decoding algorithm of polar codes called SlidingWindow(SW)SCAN(SWSCAN)algorithm is proposed,which can exactly estimate the channel state of time-varying channel at each time during SCAN decoding,even though channel parameter is unknown.Based on the SWSCAN decoding algorithm,a Weighted-Window(WW)SCAN decoding algorithm is proposed by optimizing the weight value of the window.(3)The above two adaptive decoding algorithms are proposed based on gradually varying non-stationary channels with memory,and their decoding performances are not good for channels with abrupt state changes.Therefore,a Linear-Weighting(LW)LWSCAN decoding algorithm is proposed,which mainly applies a classical method to estimate the local state of piecewise-stationary binary sources named LW algorithm to the channel estimation with abrupt state changes,it can effectively improve the decoding performance of polar codes.The above three adaptive SCAN decoding algorithms are seeded with a coarse estimate of channel state,and after each SCAN iteration,the decoders progressively refine the estimate of channel state.The experimental results demonstrate that the proposed adaptive SCAN decoders outperform the original SCAN decoder and other competitors.Meanwhile,it is verified that the proposed algorithms are robust to different choices of the initial value of channel state estimation.