Abstract
Polar codes asymptotically achieve the symmetric capacity of arbitrary binary-input discrete memoryless channels under low-complexity sequential decoding algorithms such as successive cancellation decoding. However, in their original formulation, the block length of polar codes is limited to integer powers of the dimension of the underlying polarization kernel used, thus imposing strict constraints on possible application scenarios. While leeway in the choice of kernel or concatenation with other codes mitigates this drawback to a certain extent, puncturing presents a promising approach to specify the target length of a polar code with much greater flexibility. In this paper, we present an efficient implementation of the construction of punctured polar codes based on density evolution, a crucial tool in the construction of both regular, i.e., unpunctured, as well as punctured polar codes. Our implementation of density evolution covers the construction of both regular and punctured polar codes and allows for treating the construction of both code classes in a unified framework. Using our implementation, we achieve substantial reductions in the number of density convolutions necessary for the construction of punctured polar codes and obtain tight upper bounds on the block error rates.
Highlights
Polar codes present the first channel coding scheme provably achieving the symmetric capacity of arbitrary binaryinput discrete memoryless channels (BDMCs)
We present an efficient implementation for the construction of both regular and punctured polar codes (PCs) based on a density evolution (DE), which allows treating the practical construction problem for both classes of PCs in a unified framework
In this work, we present an efficient implementation for constructing punctured PCs using DE
Summary
Polar codes present the first channel coding scheme provably achieving the symmetric capacity of arbitrary binaryinput discrete memoryless channels (BDMCs). We follow the subvector notation used in [1] and let uA = (ui)i∈A denote a subvector of u containing the information bits, where A ⊂ [N ] provides the indices of these information positions This implies a generator GN,A of the code formed by selecting rows gi, i ∈ A from the matrix GN = BN F⊗n, where BN is a bit-reversal permutation, and F as in (1) is the binary polarization kernel [1].
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
