Research On Polar Coding Theory And Practical Applications

Polar codes, recently introduced by Arikan, are the first code family that has been proven to achieve the symmetric capacity on binary-input discrete memoryless channels. Besides, due to the structural property, it needn’t an optimizing search when constructing a polar code. Therefore, polar coding theory quickly becomes an active reseach area, and is a competitive candidate in future digital communication system. This capacity-achieving code family is based on a technique called channel polarization. Shortly after the polar coding was firstly put forward, channel polarization has been applied to many other signal processing fields, such as source coding, multiple access communications, information secrecy and other settings.Although polar codes have astonishing asymptotic performance, the finite-length performance of polar codes is still unsatisfying. Besides, the underlying channels participated in the channel polarization have to share the same channel condition, and the code length of the existing polar coding is also restricted to the powers of two. On the other hand, most of the related studies on channel polarization concern the channel coding as an isolated module in the communication system without a joint optimization with other related modules (e.g. modulator, etc).This dissertation extends the polar coding theory to the practical application scenarios, and proposes some practical coding and decoding schemes. The study mainly focuses on the following three research points.1. Improved decoding schemes of polar codes. The successive cancellation (SC) decoding algorithm is redefined as a path search procedure on the code tree. By allowing more than one candidate paths to be explored during the search procedure, three improved successive cancellation (ISC) decoding algorithms are proposed:1) the successive cancellation list (SCL) decoding which performs a width-first seach on the code tree;2) the successive cancellation stack (SCS) decoding which performs a depth-first or "best-first" search on the code tree;3) the successive cancellation hybrid (SCH) decoding which is a combination of SCL and SCS that can provide a flexible configuration when the time and space complexies are limited. Furthermore, a pruning technique is also proposed to lower the complexity by reducing unnecessary path searching operations. Ultilizing the prior message that the uncoded bit sequence can pass the cyclic redundancy check (CRC), which is a general case in practical digital communication system, the performance of polar codes under the ISC decoding algorithms can be significantly improved. Performance and complexity analysis based on simulations show that, under the CRC-aided ISC decoding, polar codes can achieve even better performance than the Turbo or LDPC codes with comparable encoding and decoding complexity.2. Polar coded link adaption techniques. Channel polarization theory is extended to the case of communication over parallel channels, which allows the underlying channels participated in the channel polarization have different transition functions. Then, regarding the puncturing as transmissions of the punctured bits over virtual channels with zero capacities, a rate-compatible punctured polar (RCPP) coding scheme is proposed. Base on the RCPP codes, two polar coded HARQ transmisision schemes with Chase combining (CC) and incremental redundancy (IR), which fill the gap in the study of polar coded HARQ scheme. Numerical results show that, the polar coded schemes perform as well as those Turbo/LDPC coded schemes. In high SNR regions, the polar coded schemes can even outperform the others.3. Joint optimization of polar coding with modulation and multi-antenna transmission. Two polar coded modulation (PCM) schemes are proposed:1) bit-interleaved polar coded modulation (BIPCM), which transform the modulation channel to a set of parallel channels by a bit-level interleaver;2) PCM based on joint channel polarization, where the modulation is regarded as a special implementation of channel polarization and concatenated with the binary polar coding. Then, the multi-antenna transmission is further taken into consideration. Similar to the joint polarized PCM scheme, the MIMO transimitting and detecting can also be regarded as a special kind of channel polarization. Thus, MIMO transmission, modulation and binary polar coding form a three-stage joint channel polarization. Based on this generalized channel polarization, the proposed space-time polar coded modulation (STPCM) scheme allows a joint optimization of the binary polar coding, modulation and MIMO transmission. Furthermore, a practical solution of polar coding over the fading channel is also provided, where the fading channel is approximated by an AWGN channel with identical capacity. The simulations over the MIMO channel with Rayleigh fast and uncorrelated fading show that the proposed PCM/STPCM scheme can outperform the bit-interleaved Turbo coded scheme in all the simulated cases, where the latter is adopted in many existing communication systems.