Long Polar vs. LDPC Codes under Complexity-Constrained Decoding

2025-08-07

AI Summary

Conventional wisdom holds that polar codes are suitable only for short block lengths, while LDPC codes dominate in long-code regimes; however, practical latency constraints often limit the number of BP decoding iterations, undermining LDPC performance. Method: We propose a fixed-point LLR-based fine-grained complexity model to rigorously compare computational efficiency under realistic complexity constraints. We analyze the asymptotic complexity of SSC decoding and quantify information-processing efficiency per computational unit relative to a single BP iteration. Contribution/Results: Our analysis reveals that SSC decoding complexity grows sub–O(N log N), and its per-operation information throughput exceeds that of one BP iteration. Under comparable computational budgets, polar codes with N ≥ 1024 significantly outperform LDPC codes in bit-error-rate performance—especially in the medium-to-high SNR regime—demonstrating superior robustness and energy efficiency. This challenges the short-code-only paradigm and establishes polar codes as competitive for long-block applications under delay-sensitive constraints.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Machine Learning: Optimization
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding

Application Category

• Security and Privacy: Large-scale security measurements
• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems

Abstract

The prevailing opinion in industry and academia is that polar codes are competitive for short code lengths, but can no longer keep up with low-density parity-check (LDPC) codes as block length increases. This view is typically based on the assumption that LDPC codes can be decoded with a large number of belief propagation (BP) iterations. However, in practice, the number of iterations may be rather limited due to latency and complexity constraints. In this paper, we show that for a similar number of fixed-point log-likelihood ratio (LLR) operations, long polar codes under successive cancellation (SC) decoding outperform their LDPC counterparts. In particular, simplified successive cancellation (SSC) decoding of polar codes exhibits a better complexity scaling than $N log{N}$ and requires fewer operations than a single BP iteration of an LDPC code with the same parameters.

Problem

• Compare performance of polar vs LDPC codes under complexity constraints
• Evaluate decoding efficiency with limited belief propagation iterations
• Show polar codes outperform LDPC with simplified successive cancellation

Innovation

• Polar codes outperform LDPC under complexity constraints
• Simplified SC decoding reduces polar code complexity
• Fewer operations than LDPC belief propagation iteration