Polar Codes and Their Quantum-Domain Counterparts
arXiv:1909.09200 · doi:10.1109/COMST.2019.2937923
Abstract
Arikan's polar codes are capable of achieving the Shannon's capacity at a low encoding and decoding complexity, while inherently supporting rate adaptation. By virtue of these attractive features, polar codes have provided fierce competition to both the turbo as well as the Low Density Parity Check (LDPC) codes, making its way into the 5G New Radio (NR). Realizing the significance of polar codes, in this paper we provide a comprehensive survey of polar codes, highlighting the major milestones achieved in the last decade. Furthermore, we also provide tutorial insights into the polar encoder, decoders as well as the code construction methods. We also extend our discussions to quantum polar codes with an emphasis on the underlying quantum-to-classical isomorphism and the syndrome-based quantum polar codes.
arXiv comment35 pages, accepted for publication in IEEE Communications Surveys and Tutorials
References in corpus (32)
- Channel polarization: A method for constructing capacity-achieving codes for symmetric binary-input memoryless channels
- Good Quantum Error-Correcting Codes Exist
- LLR-based Successive Cancellation List Decoding of Polar Codes
- Correcting Quantum Errors with Entanglement
- Fast Polar Decoders: Algorithm and Implementation
- Fast and Flexible Successive-Cancellation List Decoders for Polar Codes
- Improved Successive Cancellation Decoding of Polar Codes
- Fast List Decoders for Polar Codes
- Belief Propagation List Decoding of Polar Codes
- Polar Subcodes
- Entanglement required in achieving entanglement-assisted channel capacities
- Polar codes for classical-quantum channels
- Flexible and Low-Complexity Encoding and Decoding of Systematic Polar Codes
- Tensor Networks and Quantum Error Correction
- A Split-Reduced Successive Cancellation List Decoder for Polar Codes
- Improved Successive Cancellation Flip Decoding of Polar Codes Based on Error Distribution
- Efficient Quantum Polar Coding
- Symbol-Decision Successive Cancellation List Decoder for Polar Codes
- On Metric Sorting for Successive Cancellation List Decoding of Polar Codes
- A Low-Latency List Successive-Cancellation Decoding Implementation for Polar Codes
- Polar codes for private and quantum communication over arbitrary channels
- Fast-SSC-Flip Decoding of Polar Codes
- Scalable Successive-Cancellation Hardware Decoder for Polar Codes
- The Road From Classical to Quantum Codes: A Hashing Bound Approaching Design Procedure
- Low-latency List Decoding Of Polar Codes With Double Thresholding
- A High-Throughput Architecture of List Successive Cancellation Polar Codes Decoder with Large List Size
- A Reduced Latency List Decoding Algorithm for Polar Codes
- Quantum polar codes for arbitrary channels
- Polar codes for degradable quantum channels
- Efficient Quantum Polar Codes Requiring No Preshared Entanglement
- Symbol-Based Successive Cancellation List Decoder for Polar Codes
- A Low Complexity Encoding Algorithm for Systematic Polar Codes