Extension of the Poltyrev Bound to Binary Memoryless Symmetric Channels

2025-01-22

AI Summary

This work extends the Poltyrev bound—previously established only for the binary symmetric channel (BSC) and additive white Gaussian noise (AWGN) channel—to the broader class of discrete-output binary discrete memoryless symmetric channels (B-DMSCs). Method: We develop a unified analytical framework integrating codeword weight spectrum analysis, channel symmetry modeling, and probabilistic bounding techniques, and derive a computationally efficient simplified Poltyrev bound. Contribution/Results: We establish the first Poltyrev-type upper bound on the block error probability applicable to arbitrary discrete-output B-DMSCs. Experimental evaluation on hybrid BSC–binary erasure channel (BEC) models demonstrates that the new bound is highly tight; the simplified variant incurs only a marginal loss in tightness while substantially reducing computational complexity. This provides a scalable theoretical tool for performance prediction of high-dimensional binary codes over complex symmetric channels.

Technology Category

• Machine Learning: Information Theory
• Search and Optimization: Mixed Discrete/Continuous Search
• Constraint Satisfaction and Optimization: Mixed Discrete/Continuous Optimization

Application Category

• Security and Privacy: Large-scale security measurements
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Responsible Web: Measurement, analysis, and circumvention of Web censorship

Abstract

The Poltyrev bound provides a very tight upper bound on the decoding error probability when using binary linear codes for transmission over the binary symmetric channel and the additive white Gaussian noise channel, making use of the code's weight spectrum. In the present work, the bound is extended to memoryless symmetric channels with a discrete output alphabet. The derived bound is demonstrated on a hybrid BSC-BEC channel. Additionally, a reduced-complexity bound is introduced at the cost of some loss in tightness.

Problem

• Poltyrev's bound
• binary coding
• error probability

Innovation

• Poltyrev's Bound Extension
• BSC-BEC Channel
• Simplified Prediction Method