Stitched Polar Codes

TL;DR

This work introduces stitched polar codes, a generalization of polar codes that reconfigures the polarization process by attaching additional structures to bolster the reliability of the least reliable information bits while preserving encoding/decoding complexity of $O(N\log N)$. It develops a formal stitching framework with validated coupling sequences, SC (and SC-list) decoding, and a theoretical analysis showing a reduced fraction of unpolarized bit-channels and improved polarization speed compared to regular polar codes; it also provides left- and right-stitched constructions, recursive and partially stitched methods, and scaling-law results. The authors show, both theoretically and numerically, that stitched polar codes achieve smoother performance across all lengths, solving the rate-matching degradation problem and delivering gains up to roughly $0.3$ dB at the same complexity for finite lengths. The results have practical implications for flexible code-length and rate adaptation in hardware-friendly polar coding, enabling robust performance without increased decoding complexity.

Abstract

In this paper, we introduce stitched polar codes, a novel generalization of Arıkan's regular polar codes. Our core methodology reconfigures the fundamental polarization process by stitching additional structures to enhance the reliability of less reliable information bits in the original code. This approach preserves the polar transformation structure and maintains the same encoding and decoding complexity. Thanks to the flexible configuration, stitched polar codes consistently outperform regular polar codes, effectively solving the performance degradation issue in rate-matched scenarios. Furthermore, we provide theoretical analysis on the weight spectrum and the polarization speed of stitched polar codes to prove their superiority.

Figures (35)

• Figure 1: SC decoding performance of regular and stitched (STC) polar codes with rate $R=1/2$ and BLER $=0.01$ over addictive white Gaussian noise (AWGN) channel.
• Figure 2: The factor graph representations of (a) QUP polar code and (b) stitched polar code with $N=5$ and $K=2$. The reliabilities of information bits are marked in red.
• Figure 3: Two stitching perspectives for the same stitched polar code with $N=5$ and $K=3$.
• Figure 4: The encoding process.
• Figure 5: The GA process of length-5 stitched polar code.

Theorems & Definitions (47)

• Definition 1: Punctured Code and Puncturing Pattern
• Definition 2: Shortened Code and Shortening Pattern
• Example 1
• Proposition 1
• Definition 3
• Example 2
• Example 3
• Example 4
• Definition 4
• Lemma 1