Near-Optimal Generalized Decoding of Polar-like Codes with Improved Error Detection Capabilities

Core Concepts

A framework that can exploit the tradeoff between the undetected error rate (UER) and block error rate (BLER) of polar-like codes, using a novel approximation called codebook probability. This approximation enables near-optimal joint error correction and detection, outperforming state-of-the-art methods.

Abstract

The paper presents a framework for generalized decoding of polar-like codes that can effectively balance the tradeoff between the undetected error rate (UER) and block error rate (BLER). The key component is a novel approximation called the "codebook probability", which estimates the sum of probabilities for all valid codewords given the soft-input.
The proposed approach works with any successive cancellation (SC)-based decoding method, including SC list (SCL) decoding. It relies on a threshold test that compares the ratio of the decoder output probability and the approximated codebook probability to a threshold. This enables near-optimal joint error correction and detection, outperforming the state-of-the-art Forney's generalized decoding rule for polar-like codes with dynamic frozen bits.
Simulation results demonstrate that dynamic Reed-Muller (RM) codes using the proposed generalized decoding significantly outperform CRC-concatenated polar codes decoded using SCL in both BLER and UER. The authors also discuss three potential applications of the approximated codebook probability: coded pilot-free channel estimation, bitwise soft-output decoding, and improved turbo product decoding.

Stats

The paper presents several numerical results to demonstrate the accuracy of the codebook probability approximation and the performance of the proposed joint error correction and detection scheme:

Fig. 2 shows that the approximation accurately predicts the BLER of polar-like codes with dynamic frozen constraints, while it has a mismatch for polar-like codes with static frozen bits.
Fig. 3 and Fig. 4 show that the proposed method outperforms CRC-concatenated polar codes in both BLER and UER, while maintaining the misdetection rate (MDR) below a specified threshold.
Fig. 5 demonstrates that the approximation accurately predicts the list error rate (LER) of polar-like codes with dynamic frozen constraints.
Fig. 6 and Fig. 7 show that the proposed bitwise soft-output decoding approach performs closer to the optimal BCJR decoder compared to Pyndiah's approximation.
Fig. 8 shows that the turbo product code decoder with the proposed soft-output SCL significantly outperforms the one with Pyndiah's approximation.

Quotes

"We present a framework that can exploit the tradeoff between the undetected error rate (UER) and block error rate (BLER) of polar-like codes."
"Simulation results demonstrates that, in the case of SC list (SCL) decoding, the proposed framework outperforms the state-of-art approximations from Forney's generalized decoding rule for polar-like codes with dynamic frozen bits."
"Dynamic Reed-Muller (RM) codes using the proposed generalized decoding significantly outperform CRC-concatenated polar codes decoded using SCL in both BLER and UER."

Key Insights Distilled From

Near-Optimal Generalized Decoding of Polar-like Codes

by Peih... at arxiv.org 05-03-2024

https://arxiv.org/pdf/2402.05004.pdf

Deeper Inquiries

How can the proposed codebook probability approximation be extended to other code families beyond polar-like codes

The proposed codebook probability approximation can be extended to other code families beyond polar-like codes by adapting the underlying principles to suit the characteristics of different codes. One approach is to modify the calculation of the codebook probability to account for the specific structure and properties of the new code family. For example, for LDPC codes, which are widely used in modern communication systems, the codebook probability approximation can be tailored to consider the sparse graph representation of LDPC codes and the iterative decoding process involved. By incorporating the unique features of different code families into the approximation method, it can be extended to provide accurate predictions for a broader range of codes.

What are the potential challenges and limitations in applying the generalized decoding framework to practical communication systems

Applying the generalized decoding framework to practical communication systems may face several challenges and limitations. One challenge is the computational complexity associated with calculating the codebook probability for large code lengths and high-dimensional codes. As the complexity of the decoding process increases with the size of the codebook, efficient algorithms and optimization techniques are required to ensure real-time performance in practical systems. Additionally, the accuracy of the approximation may vary depending on the specific code family and decoding algorithm used, leading to potential trade-offs between computational efficiency and decoding performance. Furthermore, the implementation of the generalized decoding framework in existing communication systems may require modifications to the hardware and software components to accommodate the new decoding rules and metrics.

Can the insights from this work be leveraged to develop novel code design and optimization techniques for improved reliability and efficiency

The insights from this work can be leveraged to develop novel code design and optimization techniques for improved reliability and efficiency in communication systems. By incorporating the codebook probability approximation into the design process, code families can be optimized to achieve a balance between error correction capability and error detection efficiency. This can lead to the development of codes with enhanced performance in terms of block error rate (BLER) and undetected error rate (UER). Furthermore, the generalized decoding framework can be used to design codes that are tailored to specific applications and channel conditions, allowing for adaptive error correction and detection strategies. Overall, the findings from this work provide a foundation for advancing the design and optimization of error-correcting codes for reliable communication systems.