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Trade-offs between Error Exponents and Excess-Rate Exponents of Typical Slepian-Wolf Codes
Ran Tamir Averbuch1, Neri Merhav1
1The Andrew and Erna Viterbi Faculty of Electrical Engineering, Technion - Israel Institute of Technology, Technion City, Haifa 3200003, Israel.
Typical random codes (TRCs) significantly reduce error probability in source coding with side information. This study proves TRCs achieve optimal performance with universal decoders, enhancing communication reliability.
Area of Science:
- Information Theory
- Communication Systems Engineering
- Coding Theory
Background:
- Source coding with side information at the decoder is crucial for efficient data transmission.
- Traditional random binning codes face limitations in error probability reduction.
- Semi-deterministic code ensembles offer a potential improvement.
Purpose of the Study:
- To investigate the performance of typical random codes (TRCs) in source coding with side information.
- To analyze the error and excess-rate exponents of semi-deterministic code ensembles.
- To demonstrate the attainability of optimal decoding performance using universal decoders.
Main Methods:
- Analysis of a semi-deterministic code ensemble, a variant of random binning.
- Derivation and comparison of error exponents for random binning and TRCs.
- Evaluation of universal decoders, including the stochastic likelihood decoder with empirical entropy metric.
- Characterization of trade-offs between error and excess-rate exponents.
Main Results:
- Error probability dramatically decreases in the studied semi-deterministic code ensemble.
- The error exponents of random binning and TRCs are shown to be equal in specific cases.
- Optimal decoding performance is achievable with universal decoders.
- For correlated sources, both error and excess-rate probabilities vanish exponentially with blocklength.
Conclusions:
- Typical random codes offer significant advantages in reducing error probability for source coding with side information.
- Universal decoders can achieve the same performance as optimal decoders in this context.
- The study provides a characterization of the optimal rate function and trade-offs for semi-deterministic codes.
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