On the exact decoding error probability exponent of the random coding on BSC
arXiv:2605.1999123.1
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Provides a theoretical result for information theory, but is incremental as it refines known bounds for a specific channel model.
The paper derives the exact decoding error probability exponent for random coding over a binary symmetric channel, using new results on the distribution of a sum of random variables.
For the information transmission over a binary symmetric channel the random coding is used. The transmission of exponential number of messages is considered. The exact decoding error probability exponent is derived. The proof is based on the new results on the distribution of a certain sum of random variables.