Successive Cancellation Decoder for Very Long Polar Codes

Polar codes are a family of error correcting codes that achieves the symmetric capacity of memoryless channels when the code length N tends to infinity. However, moderate code lengths are required in most of wireless digital applications to limit the decoding latency. In some other applications, such as optical communications or quantum key distribution, the latency introduced by very long codes is not an issue. The main challenge is to design codes with the best error correction capability, a tractable complexity and a high throughput. In such a context, SC decoding is an interesting solution because its performance improves with N while the computational complexity scales almost linearly. In this paper, we propose to improve the scalability of SC decoders thanks to four architectural optimizations. The resulting SC decoder is implemented on an FPGA device and favorably compares with state-of-the-art scalable SC decoders. Moreover, a 222 polar code SC decoder is implemented on a Stratix-5 FPGA. This code length is twice larger than the ones achieved in previous works. To the best of our knowledge, this is the first architecture for which a N = 4 million bits polar code can be actually decoded on a reconfigurable circuit.