Multi-kernel polar codes, which are constructed by different sizes of kernels make the traditional polar codes have more flexible code length. In this paper, we extend the multi-kernel polar codes to
5×5 kernels including kernel design, code design, and fast decoding. First, we construct a new
5×5 kernel, which has the maximum polarization rate. The first row of this kernel is all-one vector, which enable us to seek the relation between node modification and distance property of multi-kernel polar codes. Second, we modify the repetition (REP) nodes to this kernel, which can increase the distance property of the constructed polar codes, improve the decoding performance and reduce memory requirements during the fast decoding. In addition, we find this REP node modification can be generalized when multi-kernel polar codes constructed by kernels, which the first row is all-one vector. Third, we prove the four kinds of basic nodes (Rate-1 node, Rate-0 nodes, Repetition (REP) nodes, and Single-Parity check (SPC) nodes) of fast decoding are suitable for this kernel. Moreover, we generalize the Generalized Parity-Check (G-PC) nodes and the Generalized Repetition (GREP) nodes, which are suitable for multi-kernel polar codes constructed by any size of kernels and any order of kernels. The G-PC and G-REP nodes can further accelerate the decoding speed. By simulations, we show that our modification improves the error-rate performance of the fast decoding. Meanwhile, the fast decoding of our multi-kernel polar codes has at least 68. 4% reduced latency compared with the traditional SC decoder in all cases considered where frame lengths are (
80,135,400,675). Index Terms-Multi-kernel polar codes, node modification, fast decoding,
5×5 kernel matrix
Multi-kernel polar codes, which are constructed by different sizes of kernels make the length of the traditional polar code more flexible. In this paper, we extend the multi-kernel polar codes to 5×5 kernels including kernel design, code design, and fast decoding. First, we construct a new 5×5 kernel with the maximum polarization rate. The first row of this kernel is an all-one vector, which enable us to find the relation between node modification and distance property of multi-kernel polar codes. Second, we modify the repetition (REP) nodes to the new 5×5 kernel, which can increase the distance property of the constructed polar codes, improve the decoding performance and reduce memory requirements during the fast decoding. In addition, we find our REP node modification can be generalized to multi-kernel polar codes when the first row of the used kernels is all-one vector. Third, we prove the four kinds of basic nodes (Rate-1 node, Rate-0 nodes, Repetition (REP) nodes, and Single-Parity check (SPC) nodes) of fast decoding are suitable for the new kernel. Moreover, we generalize the Generalized Parity-Check (G-PC) nodes and the Generalized Repetition (GREP) nodes, which are suitable for multi-kernel polar codes constructed by any size of kernels and any order of kernels. By simulations, we show that our modification improves the error-rate performance of the fast decoding. Meanwhile, the fast decoding of our multi-kernel polar codes has at least 68.4% latency reduction compared with the traditional SC decoder in all cases considered where code lengths are 80, 135, 400, and 675.
Polar codes have gained significant a ttention in recent years due to their superior performance, making them an attractive choice for use in modern communication systems. In this paper, we present a novel approach for implementing a fast decoding method for polar codes with additional nodes. Specifically, we propose a modification of the fast decoding method with bit-flipping capability, called the GSCLAF, which is designed to improve the correction capability of the decoder. To achieve this, we consider additional nodes of five types, which are obtained by a combination of basic generalized nodes, namely information, frozen, SPC, and REP nodes. To evaluate the performance of our proposed algorithm, numerical experiments were conducted using the 5G NR polar code. The results of these experiments demonstrate the effectiveness of GSCLAF relative to other popular polar decoding algorithms. Overall, our proposed algorithm provides a powerful tool for improving the decoding performance of polar codes with additional nodes, making it a promising solution for modern communication systems that require high data rates and reliable communication.
Window decoding is useful for decoding polar codes defined by kernels that do not have Arıkan's original form. We modify arbitrary polarization kernels of size 2t × 2t to reduce the time complexity of window decoding. This modification is based on the permutation of the columns of the kernel. This method is applied to some of the kernels constructed in the literature of size 16 and 32, with different error exponents and scaling exponents such as eNBCH kernel. It is shown that this method reduces the complexity of the window decoding significantly without affecting the performance.
We propose a generalized construction for binary polar codes based on mixing multiple kernels of different sizes in order to construct polar codes of block lengths that are not only powers of integers. This results in a multi-kernel polar code with very good performance while the encoding complexity remains low and the decoding follows the same general structure as for the original Arikan polar codes. The construction provides numerous practical advantages as more code lengths can be achieved without puncturing or shortening. We observe numerically that the error-rate performance of our construction outperforms
We propose a generalized construction for binary polar codes based on mixing multiple kernels of different sizes in order to construct polar codes of block lengths that are not only powers of integers. This results in a multi kernel polar code with very good performance while the encoding complexity remains low and the decoding follows the same general structure as for the original Arikan polar codes. The construction provides numerous practical advantages as more code lengths can be achieved without puncturing or shortening. We observe numerically that the error-rate performance of our construction outperforms stateof the-art constructions using puncturing methods.