Algorithm

Discrete mathematics

Galois theory

Telecommunications

Set (abstract data type)

Parallel computing

Computer science

Polar code

Code (set theory)

Soft-decision decoder

Decoding methods

Physics

Mathematics

Astronomy

Polar

Mathematical analysis

Tree (set theory)

Programming language

Error detection and correction

Finite field

Wireless

Throughput

Nonbinary polar codes defined over Galois field GF(q) have shown improved error-correction performance than binary polar codes using successive-cancellation list (SCL) decoding. However, nonbinary operations are complex and a direct-mapped decoder results in a low throughput, representing difficulties for practical adoptions. In this work, we develop, to the best of our knowledge, the first hardware implementation for nonbinary SCL polar decoding. We present a high-throughput decoder architecture using a split-tree algorithm. The sub-trees are decoded in parallel by smaller sub-decoders with a reconciliation stage to maintain constraints between sub-trees. A skimming algorithm is proposed to reduce the reconciliation complexity for further improved throughput. The split-tree nonbinary SCL (S-NBSCL) polar decoder is prototyped using a 28nm CMOS technology for a (128,64) polar code over GF(256). The decoder delivers 26.1 Mb/s throughput, 11.65 Mb/s/mm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> area efficiency and 28.8 nJ/b energy efficiency, outperforming the direct-mapped decoder by 10.3×, 4.4× and 2.7×, respectively, while achieving excellent error-correction performance.

High-Throughput Split-Tree Architecture for Nonbinary SCL Polar Decoder