Problem
Research questions and friction points this paper is trying to address.
descriptive complexity
source coding
joint source-channel coding
polar codes
lossless compression
Polar Complexity: A New Descriptive Complexity with Applications to Source and Joint Source-Channel Coding
🤖 AI Summary
This work addresses the challenge of measuring descriptive complexity for finite-length binary sequences and achieving efficient lossless compression without prior knowledge of source statistics. It introduces a novel metric termed “polarization complexity,” defined as the shortest code length that enables exact reconstruction via polar compression and successive cancellation decoding. Building upon this notion, the authors devise a two-stage polar source coding scheme that guarantees strictly lossless, prefix-free compression without requiring source priors. Furthermore, they propose an adaptive dual-polarization joint source-channel coding architecture that allows flexible trade-offs between performance and computational complexity. Theoretical analysis demonstrates that the proposed source coder asymptotically achieves normalized average code length approaching the entropy rate under binary memoryless sources. Simulations confirm that the joint coding scheme outperforms existing polarization-based baselines.
📝 Abstract
This paper first presents a new approach to evaluating the descriptive complexity of finite-length binary sequences. Specifically, we investigate the sequence-wise recovery behavior induced by polar compression and successive cancellation decoding (SCD), and define the polar complexity of a sequence as the minimum polar-compression length (PCL) required for its exact reconstruction. To compute the polar complexity efficiently, we further develop both a bisection-search algorithm and a low-complexity estimation method. We then propose a polar-based two-stage source coding scheme, in which each source sequence is represented by its polar complexity followed by the corresponding polar-compressed sequence. The proposed scheme is strictly lossless and prefix-free. In addition, for BMSs, the normalized average compression length of the proposed scheme can asymptotically approach the source entropy under certain conditions. Simulation results further demonstrate that the scheme can operate without prior knowledge of the source statistics and remains robust across different source distributions. Finally, we integrate the proposed polar source coding with polar channel coding to develop an adaptive double-polar joint source-channel coding (JSCC) scheme, where the encoder and decoder share a predefined set of candidate PCLs to balance error performance and decoding complexity. We formulate the design of the candidate-PCL set as an optimization problem and solve it efficiently via dynamic programming. Simulation results show that the proposed adaptive double-polar JSCC scheme provides a flexible performance-complexity tradeoff and outperforms existing polar-code-based JSCC baselines.
Innovation
Methods, ideas, or system contributions that make the work stand out.
polar complexity
polar source coding
joint source-channel coding
successive cancellation decoding
adaptive PCL optimization
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