Research On Design Of Polar Codes Concatenations And Its Applications

Polar codes which are construced based on channel polarization are a new type of channel coding.Channel polarization is an operation by which one manufactures out of N=2n(n is a positive integer)independent copies of a given binary-input discrete memo-ryless channel(B-DMC)W a second set of polarized channels,and the polarized channels show a polarization in the capacity.As N goes to infinity,capacities of some polarized channels tend towards 1(these channels are named as no-noise channels)while capacities of others tend towards 0(these channels are named as full-noise channels),and the frac-tion of no-noise channels goes to the capacity of W I(W).Polar encoding is obtained by setting information bits over no-noise channels and frozen bits which are known to both transmitter and receiver over full-noise channels.Thus polar codes is a family of prove-able capacity-achieving codes.Besides,polar codes have an explicit construction method and a regular encoding structure.Therefore,researching on the design and application of polar codes have great research and application values.Polar codes with successive cancellation(SC)decoding can achieve Shannon capac-ity when code length is infinite.However,in practical applications,the error rate perfor-mance of polar codes with finite length is unsatisfactory under the SC decoder.Succes-sive sancellation list(SCL)decoder and Cyclic Redundancy Check aided SCL(CASCL)decoder,improved versions of SC decoder,can approach the performance of maximum-likelihood(ML)decoding at the cost of higher memory requirement and decoding com-plexity.Apart from SC decoding,belief propagation(BP)decoding is also identied as an improtant decoding method for polar codes.Since BP decoding can be easily parallelized,low latency and high throughput implementations are possible.However,the performance of BP decoding is still inferior to that of SCL decoding.One reason is that bit-channels of finite-length polar codes are not fully polarized,and the negative influences from semi-polarized channels are not negligible.Besides,length of polar codes is limited to be a power of 2,thus how to construct polar codes with flexible length is still a problem.Also,the j oint optimizations of polar codes with hybrid automatic retransmission query(HARQ)and high level modulations need to be further studied.Trying to address these issues,this dissertation proposed new methods and carried out simulation experiments,includes1.To solve the problem of high complexity of SCL decoding,an interleaved concate-nation scheme of polar codes with non-binary low-density parity check(LDPC)codes is proposed,in which segment successive cancellation list decoder is carried out in parallel for inner polar codes to reduce decoding storage.Moreover,an im-proved SCL decoder with a selective extension is proposed for the concatenated polar codes for a better error-correcting performance.Simulation results show that the proposed polar code with the designed decoder can be comparable with pure polar codes with SCL decoding,but require lower decoding storage.2.To improve the error correction performance of finite-length polar code with belief propagation(BP)decoding,we consider using an outer LDPC code to protect in-termediate bit-channels.We propose a bit mapping method between LDPC coded bits and polarized channels for a better performance.Simulation results show that,the concatenated polar codes with bit mapping outperform pure polar codes with BP decoding about 0.5 dB.3.We consider the joint optimization of polar codes with BP decoding and high level modulations,and propose a mapping algorithm to assign coded bits to different bit positions of the transmitted symbols.The proposed mapping takes into account the impact of both unequal error protection of high-order modulator and stopping sets of polar code.Simulation result shows that the designed mapping scheme pro-vides better performance than that of the conventional random mapping scheme.Besides,to meet the code-length requirements brought by different modulations,we introduce a method to construct flexible length polar code(FLPC),by coupling two short length polar codes with a re333peawt accumulate(RA)code.Simulation results show that a combination of the proposed FLPC and designed bit mapping with BP decoding provides 1 dB performance gain over the polar coded modulation scheme with SC decoding.4.We studied the joint design of systematic polar codes and HARQ,and propose a scheme to enable IR-HARQ with low decoding complexity based on multiple CRC.Simulation result shows that the designed HARQ scheme has lower decoding com-plexity than traditional polar coded HARQ scheme,and it is applicable for internet of things applications.