An Implementation of List Successive Cancellation Decoder with Large List Size for Polar Codes

Polar codes are the first class of forward error correction (FEC) codes with a provably capacity-achieving capability. Using list successive cancellation decoding (LSCD) with a large list size, the error correction performance of polar codes exceeds other well-known FEC codes. However, the hardware complexity of LSCD rapidly increases with the list size, which incurs high usage of the resources on the field programmable gate array (FPGA) and significantly impedes the practical deployment of polar codes. To alleviate the high complexity, in this paper, two low-complexity decoding schemes and the corresponding architectures for LSCD targeting FPGA implementation are proposed. The architecture is implemented in an Altera Stratix V FPGA. Measurement results show that, even with a list size of 32, the architecture is able to decode a codeword of 4096-bit polar code within 150 us, achieving a throughput of 27MbpsComment: 4 pages, 4 figures, 4 tables, Published in 27th International Conference on Field Programmable Logic and Applications (FPL), 201

On Path Memory in List Successive Cancellation Decoder of Polar Codes

Polar code is a breakthrough in coding theory. Using list successive cancellation decoding with large list size L, polar codes can achieve excellent error correction performance. The L partial decoded vectors are stored in the path memory and updated according to the results of list management. In the state-of-the-art designs, the memories are implemented with registers and a large crossbar is used for copying the partial decoded vectors from one block of memory to another during the update. The architectures are quite area-costly when the code length and list size are large. To solve this problem, we propose two optimization schemes for the path memory in this work. First, a folded path memory architecture is presented to reduce the area cost. Second, we show a scheme that the path memory can be totally removed from the architecture. Experimental results show that these schemes effectively reduce the area of path memory.Comment: 5 pages, 6 figures, 2 table

Comparison of Polar Decoders with Existing Low-Density Parity-Check and Turbo Decoders

Polar codes are a recently proposed family of provably capacity-achieving error-correction codes that received a lot of attention. While their theoretical properties render them interesting, their practicality compared to other types of codes has not been thoroughly studied. Towards this end, in this paper, we perform a comparison of polar decoders against LDPC and Turbo decoders that are used in existing communications standards. More specifically, we compare both the error-correction performance and the hardware efficiency of the corresponding hardware implementations. This comparison enables us to identify applications where polar codes are superior to existing error-correction coding solutions as well as to determine the most promising research direction in terms of the hardware implementation of polar decoders.Comment: Fixes small mistakes from the paper to appear in the proceedings of IEEE WCNC 2017. Results were presented in the "Polar Coding in Wireless Communications: Theory and Implementation" Worksho

A Multi-Kernel Multi-Code Polar Decoder Architecture

Polar codes have received increasing attention in the past decade, and have been selected for the next generation of wireless communication standard. Most research on polar codes has focused on codes constructed from a $2\times2$ polarization matrix, called binary kernel: codes constructed from binary kernels have code lengths that are bound to powers of $2$. A few recent works have proposed construction methods based on multiple kernels of different dimensions, not only binary ones, allowing code lengths different from powers of $2$. In this work, we design and implement the first multi-kernel successive cancellation polar code decoder in literature. It can decode any code constructed with binary and ternary kernels: the architecture, sized for a maximum code length $N_{max}$, is fully flexible in terms of code length, code rate and kernel sequence. The decoder can achieve frequency of more than $1$ GHz in $65$ nm CMOS technology, and a throughput of $615$ Mb/s. The area occupation ranges between $0.11$ mm$^2$ for $N_{max}=256$ and $2.01$ mm$^2$ for $N_{max}=4096$. Implementation results show an unprecedented degree of flexibility: with $N_{max}=4096$, up to $55$ code lengths can be decoded with the same hardware, along with any kernel sequence and code rate