Asymmetric Construction of Low-Latency and Length-Flexible Polar Codes

Polar codes are a class of capacity-achieving error correcting codes that have been selected for use in enhanced mobile broadband in the 3GPP 5th generation (5G) wireless standard. Most polar code research examines the original Arikan polar coding scheme, which is limited in block length to powers of two. This constraint presents a considerable obstacle since practical applications call for all code lengths to be readily available. Puncturing and shortening techniques allow for flexible polar codes, while multi-kernel polar codes produce native code lengths that are powers of two and/or three. In this work, we propose a new low complexity coding scheme called asymmetric polar coding that allows for any arbitrary block length. We present details on the generator matrix, frozen set design, and decoding schedule. Our scheme offers flexible polar code lengths with decoding complexity lower than equivalent state-of-the-art length-compatible approaches under successive cancellation decoding. Further, asymmetric decoding complexity is directly dependent on the codeword length rather than the nearest valid polar code length. We compare our scheme with other length matching techniques, and simulations are presented. Results show that asymmetric polar codes present similar error correction performance to the competing schemes, while dividing the number of SC decoding operations by up to a factor of 2 using the same codeword lengthComment: To appear in IEEE International Conference on Communications 2019 (Submitted October 12, 2018), 6 page

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

Cooperative Punctured Polar Coding (CPPC) Scheme Based on Plotkin’s Construction

A new cooperative punctured polar coding (CPPC) scheme with multi joint successive cancellation (MJSC) decoding at the destination is proposed, which may be obtained by applying puncturing algorithm to cooperative polar coding scenario. In this proposed algorithm we generate a cooperative scheme for punctured polar codes with various code lengths by employing the reduction of the general polarizing matrix combined with the cooperative construction to match the multilevel characteristics of polar codes. Punctured polar codes which are a class of polar codes can support a wide range of lengths for a given rate. Hence in our CPPC scheme, the punctured polar codes can be first constructed by eliminating some of the frozen bits such that the values of the punctured bits are known to the decoder. Then the proposed coded cooperative construction is employed to match the Plotkin’s construction between the two relay nodes. This scheme has low encoding and decoding complexity since it can be encoded and decoded in a similar way as a classical polar code. The CPPC scheme offers a cooperative coding which not only improves the data rate of the cooperative system, but also improves the overall bit error rate performance. Numerical results show that cooperative punctured polar codes constructed by our approach perform much better than those by the conventional direct approach

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