Enhancing Iterative Decoding of Polar-like Code Constructions

点击翻译按钮获取中文摘要

Over the past 60 years, the field of channel coding has evolved from simple error detection through parity bit checking to powerful error correction using dedicated algebraic codes or concatenated coding schemes in conjunction with their respective (iterative) decoders. Those schemes can approach the theoretical capacity limits very closely. While most efforts over the past decade have focused on low-density parity-check (LDPC) codes, or, more recently, their spatially coupled offsprings, this proposal is about studying and enhancing another important development in the field, referred to as "polar codes", introduced by E. Arikan in 2008. He proved that polar codes can achieve capacity of any symmetric Binary Input-Discrete Memoryless Channel (BI-DMC) under Successive Cancellation (SC) decoding for infinite codeword length. As opposed to other "random-like" codes with close-to-capacity performance, polar codes have a very regular (algebraic) structure, opening up the potential for efficient low-complexity hardware implementations; this becomes particularly evident when accounting for the routing overhead in silicon chip technology, which may easily become prohibitive for iterative decoders of state-of-the-art LDPC codes. While it is instructive to realize that polar codes are closely related to Reed--Muller (RM) Codes, their sequential SC decoding algorithm (and thus the selection of the, so called, "frozen" bit channels) follow a quite different approach, leading to many attractive research questions. In this proposal, we seek to find a more comprehensive understanding of belief propagation decoding (BP) for polar codes, to enhance the BER performance of finite-length polar (and polar-like) codes, and to reduce computational complexity and latency of decoding by paving the way to highly parallelized decoder implementations. For this, we need to design polar codes tailored to BP decoding, deviating from the traditional approaches that assume SC decoding. Also, improved analysis tools are essential for better understanding the dynamics of the iterative BP decoder, such as "scattered" Extrinsic Information Transfer (EXIT) charts or density evolution (DE). Moreover, by extending the basic polar code structure, it is possible to obtain novel "polar-like" codes with improved BER performance under iterative BP decoding. First attempts using concatenation/augmentation approaches with auxiliary graph-based codes or applying the concept of spatial coupling turned out to be promising. Combining the BP decoder with a list concept, akin to the successive cancellation list decoder, and the combination of improved BP decoding strategies with channel interfaces such as higher-order modulation for communicating over scalar and vector (MIMO) channels, complement the selection of open research questions for progressing the field.