Low-Complexity Puncturing and Shortening of Polar Codes

In this work, we address the low-complexity construction of shortened and punctured polar codes from a unified view. While several independent puncturing and shortening designs were attempted in the literature, our goal is a unique, low-complexity construction encompassing both techniques in order to achieve any code length and rate. We observe that our solution significantly reduces the construction complexity as compared to state-of-the-art solutions while providing a block error rate performance comparable to constructions that are highly optimized for specific lengths and rates. This makes the constructed polar codes highly suitable for practical application in future communication systems requiring a large set of polar codes with different lengths and rates.Comment: to appear in WCNC 2017 - "Polar Coding in Wireless Communications: Theory and Implementation" Worksho

A Balanced Tree Approach to Construction of Length-Compatible Polar Codes

From the perspective of tree, we design a length-flexible coding scheme. For an arbitrary code length, we first construct a balanced binary tree (BBT) where the root node represents a transmitted codeword, the leaf nodes represent either active bits or frozen bits, and a parent node is related to its child nodes by a length-adaptive (U+V|V) operation. Both the encoding and the successive cancellation (SC)-based decoding can be implemented over the constructed coding tree. For code construction, we propose a signal-to-noise ratio (SNR)-dependent method and two SNR-independent methods, all of which evaluate the reliabilities of leaf nodes and then select the most reliable leaf nodes as the active nodes. Numerical results demonstrate that our proposed codes can have comparable performance to the 5G polar codes. To reduce the decoding latency, we propose a partitioned successive cancellation (PSC)-based decoding algorithm, which can be implemented over a sub-tree obtained by pruning the coding tree. Numerical results show that the PSC-based decoding can achieve similar performance to the conventional SC-based decoding.Comment: 30 pages, 10 figure

Polar Codes and LDPC Codes in 5G New Radio

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