Performance Of Polar Codes Research Articles

Improved Successive Cancellation Decoding of Polar Codes

As improved versions of the successive cancellation (SC) decoding algorithm, the successive cancellation list (SCL) decoding and the successive cancellation stack (SCS) decoding are used to improve the finite-length performance of polar codes. In this paper, unified descriptions of the SC, SCL, and SCS decoding algorithms are given as path search procedures on the code tree of polar codes. Combining the principles of SCL and SCS, a new decoding algorithm called the successive cancellation hybrid (SCH) is proposed. This proposed algorithm can provide a flexible configuration when the time and space complexities are limited. Furthermore, a pruning technique is also proposed to lower the complexity by reducing unnecessary path searching operations. Performance and complexity analysis based on simulations shows that under proper configurations, all the three improved successive cancellation (ISC) decoding algorithms can approach the performance of the maximum likelihood (ML) decoding but with acceptable complexity. With the help of the proposed pruning technique, the time and space complexities of ISC decoders can be significantly reduced and be made very close to those of the SC decoder in the high signal-to-noise ratio regime.

Efficient Design and Decoding of Polar Codes

Polar codes are shown to be instances of both generalized concatenated codes and multilevel codes. It is shown that the performance of a polar code can be improved by representing it as a multilevel code and applying the multistage decoding algorithm with maximum likelihood decoding of outer codes. Additional performance improvement is obtained by replacing polar outer codes with other ones with better error correction performance. In some cases this also results in complexity reduction. It is shown that Gaussian approximation for density evolution enables one to accurately predict the performance of polar codes and concatenated codes based on them.

CRC-Aided Decoding of Polar Codes

CRC (cyclic redundancy check)-aided decoding schemes are proposed to improve the performance of polar codes. A unified description of successive cancellation decoding and its improved version with list or stack is provided and the CRC-aided successive cancellation list/stack (CA-SCL/SCS) decoding schemes are proposed. Simulation results in binary-input additive white Gaussian noise channel (BI-AWGNC) show that CA-SCL/SCS can provide significant gain of 0.5 dB over the turbo codes used in 3GPP standard with code rate 1/2 and code length 1024 at the block error probability (BLER) of 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-4</sup> . Moreover, the time complexity of CA-SCS decoder is much lower than that of turbo decoder and can be close to that of successive cancellation (SC) decoder in the high SNR regime.

Inside View

Researchers in China have used a technique called successive cancellation stack to improve the performance of polar codes. Even in high signal-to-noise ratio systems, the system offers low complexity and state-of-the-art performance. Kai Niu of the Beijing University of Posts and Telecommunications in China tells us more.

List successive cancellation decoding of polar codes

A list successive cancellation (LSC) decoding algorithm to boost the performance of polar codes is proposed. Compared with traditional successive cancellation decoding algorithms, LSC simultaneously produces at most L locally best candidates during the decoding process to reduce the chance of missing the correct codeword. The complexity of the proposed algorithm is O(LNlog N), where N and L are the code length and the list size, respectively. Simulation results of LSC decoding in the binary erasure channel and binary-input additive white Gaussian noise channel show a significant performance improvement.

Stack decoding of polar codes

A successive cancellation stack (SCS) decoding algorithm is proposed to improve the performance of polar codes. Unlike the conventional successive cancellation decoder which determines the bits successively with a local optimal strategy, the SCS algorithm stores a number of candidate partial paths in an ordered stack and tries to find the global optimal estimation by searching along the best path in the stack. Simulation results in the binary-input additive white Gaussian noise channel show that the SCS algorithm has the same performance as the successive cancellation list (SCL) algorithm and can approach that of the maximum likelihood algorithm. Moreover, the time complexity of the SCS decoder is much lower than that of the SCL and can be very close to that of the SC in the high SNR regime.

Performance of Polar Codes with the Construction using Density Evolution

Polar coding, proposed by Arikan, makes it possible to construct capacity-achieving codes for symmetric binary-input discrete memoryless channels, with low encoding and decoding complexity. Complexity of the originally proposed code construction method, however, grows exponentially in the block-length unless a channel is the binary erasure channel. Recently, the authors have proposed a new capacity-achieving code construction method with linear complexity in the block-length for arbitrary symmetric binary-input memoryless channels. In this letter, we evaluate performance of polar codes designed with the new construction method, and compare it with that of the codes constructed with another heuristic method with linear complexity proposed by Arikan.