Fast Decoding of Multi-Kernel Polar Codes

Abstract

Polar codes are a class of linear error correction codes which provably attain channel capacity with infinite codeword lengths. Finite length polar codes have been adopted into the 5th Generation 3GPP standard for New Radio, though their native length is limited to powers of 2. Utilizing multiple polarizing matrices increases the length flexibility of polar codes at the expense of a more complicated decoding process. Successive cancellation (SC) is the standard polar decoder and has time complexity O(N log N ) due to its sequential nature. However, some patterns in the frozen set mirror simple linear codes with low latency decoders, which allows for a significant reduction in SC latency by pruning the decoding schedule. Such fast decoding techniques have only previously been used for traditional Arıkan polar codes, causing multi-kernel polar codes to be an impractical length-compatibility technique with no fast decoders available. We propose fast simplified successive cancellation decoding node patterns, which are compatible with polar codes constructed with both the Arıkan and ternary kernels, and generalization techniques. We outline efficient implementations, made possible by imposing constraints on ternary node parameters. We show that fast decoding of multi-kernel polar codes has at least 72% reduced latency compared with an SC decoder in all cases considered where codeword lengths are (96, 432, 768, 2304).

Low-Latency Multi-Kernel Polar Decoders

“…Fast-SSC decoding of multi-kernel polar codes is investigated in [23]. It is proved in [23] that R0, R1 and SPC (R = N −1 N ) nodes for ternary kernel can be computed using the same method as for binary kernel.…”

“…Fast-SSC decoding of multi-kernel polar codes is investigated in [23]. It is proved in [23] that R0, R1 and SPC (R = N −1 N ) nodes for ternary kernel can be computed using the same method as for binary kernel. The mixed repetition node, however, has a different decoding rule and it is categorized into three groups for the ternary kernel.…”

“…In this paper, we refer to this group as REP T . More detail on decoding steps of each node is available in [23].…”

“…There are three functions proposed in [13] that are added to this group. • Group E Patterns: As mentioned in Section II-D, ternary fast-SSC algorithm is investigated in [23]. However, they have considered some constraints on each group of REP T that limits the appearance of repetition nodes in the polar tree.…”

A simplified decoding algorithm for multi-CRC polar codes

“…However, the existing stochastic BP decoders suffer from a relatively long decoding latency, resulting in low hardware efficiency. Meanwhile, sphere-decoding tree searches [20 -22] and other fast decoding algorithms [23,24] were proposed, respectively. Deep learning was applied to decoding a polar code with respect to numerous configurations: the number of hidden layers, the number of nodes for each layer, and activation functions [25].…”