The Birthday Problem and Zero-Error List Codes

Parham Noorzad, Michelle Effros, Michael Langberg, Victoria Kostina

نتاج البحث: نشر في مجلةمقالةمراجعة النظراء


A key result of classical information theory states that if the rate of a randomly generated codebook is less than the mutual information between the channel's input and output, then the probability that that codebook has negligible error goes to one as the blocklength goes to infinity. In an attempt to bridge the gap between the probabilistic world of classical information theory and the combinatorial world of zero-error information theory, this work derives necessary and sufficient conditions on the rate so that the probability that a randomly generated codebook operated under list decoding (for any fixed list size) has zero error probability goes to one as the blocklength goes to infinity. Furthermore, this work extends the classical birthday problem to an information-theoretic setting, which results in the definition of a 'noisy' counterpart of Rényi entropy, analogous to how mutual information can be considered a noisy counterpart of Shannon entropy.

اللغة الأصليةالإنجليزيّة
رقم المقال9500216
الصفحات (من إلى)5791-5803
عدد الصفحات13
دوريةIEEE Transactions on Information Theory
مستوى الصوت67
رقم الإصدار9
المعرِّفات الرقمية للأشياء
حالة النشرنُشِر - سبتمبر 2021
منشور خارجيًانعم

ملاحظة ببليوغرافية

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© 1963-2012 IEEE.


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