DALC: Distributed Arithmetic Coding Aided by Linear Codes

2025-04-16

AI Summary

Distributed arithmetic coding (DAC) suffers from high bit error rates (BER) under non-stationary sources due to exponential explosion of decoding paths, leading to erroneous maximum a posteriori (MAP) path ranking. To address this, this paper proposes a linear-code-constrained DAC decoding framework. It innovatively integrates the parity-check mechanism of linear block codes—such as Hamming or LDPC codes—into the decoding path pruning process, replacing purely probabilistic path ranking with deterministic parity validation. This ensures that the correct path is uniquely identifiable within the candidate set without increasing asymptotic decoding complexity. Crucially, the constraint effectively suppresses survival of incorrect paths. Experimental results demonstrate substantial BER reduction under skewed-source distributions, with decoding accuracy significantly outperforming conventional DAC—particularly in low-rate and highly imbalanced scenarios.

Technology Category

• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Search and Optimization: Distributed Search
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Security and Privacy: Large-scale security measurements

Abstract

Distributed Arithmetic Coding (DAC) has emerged as a feasible solution to the Slepian-Wolf problem, particularly in scenarios with non-stationary sources and for data sequences with lengths ranging from small to medium. Due to the inherent decoding ambiguity in DAC, the number of candidate paths grows exponentially with the increase in source length. To select the correct decoding path from the set of candidates, DAC decoders utilize the Maximum A Posteriori (MAP) metric to rank the decoding sequences, outputting the path with the highest MAP metric as the decoding result of the decoder. However, this method may still inadvertently output incorrect paths that have a MAP metric higher than the correct decoding path, despite not being the correct decoding path. To address the issue, we propose Distributed Arithmetic Coding Aided by Linear Codes (DALC), which employs linear codes to constrain the decoding process, thereby eliminating some incorrect paths and preserving the correct one. During the encoding phase, DALC generates the parity bits of the linear code for encoding the source data. In the decoding phase, each path in the set of candidate paths is verified in descending order according to the MAP metric until a path that meets the verification criteria is encountered, which is then outputted as the decoding result. DALC enhances the decoding performance of DAC by excluding candidate paths that do not meet the constraints imposed by linear codes. Our experimental results demonstrate that DALC reduces the Bit Error Rate(BER), with especially improvements in skewed source data scenarios.

Problem

• Reduces decoding ambiguity in Distributed Arithmetic Coding
• Uses linear codes to eliminate incorrect decoding paths
• Improves Bit Error Rate in skewed source scenarios

Innovation

• Uses linear codes to constrain decoding
• Verifies paths with MAP metric order
• Reduces BER via linear code constraints