Journal ArticleDOI
Channel Coding Rate in the Finite Blocklength Regime
Reads0
Chats0
TLDR
It is shown analytically that the maximal rate achievable with error probability ¿ isclosely approximated by C - ¿(V/n) Q-1(¿) where C is the capacity, V is a characteristic of the channel referred to as channel dispersion, and Q is the complementary Gaussian cumulative distribution function.Abstract:
This paper investigates the maximal channel coding rate achievable at a given blocklength and error probability. For general classes of channels new achievability and converse bounds are given, which are tighter than existing bounds for wide ranges of parameters of interest, and lead to tight approximations of the maximal achievable rate for blocklengths n as short as 100. It is also shown analytically that the maximal rate achievable with error probability ? isclosely approximated by C - ?(V/n) Q-1(?) where C is the capacity, V is a characteristic of the channel referred to as channel dispersion , and Q is the complementary Gaussian cumulative distribution function.read more
Citations
More filters
Posted Content
CHIRRUP: a practical algorithm for unsourced multiple access
TL;DR: In this article, a multiuser detection of binary chirps which are simply codewords in the second order Reed Muller code is presented. And the worst-case complexity of the basic chirp reconstruction algorithm is O(nK(log_2 n + K) where n is the number of active users and k is the total number of users.
Journal ArticleDOI
Polar Coding for Non-Stationary Channels
TL;DR: In this article, the authors considered the problem of polar coding for a non-stationary sequence of independent BMS channels and constructed a polar code of length ε and rate ε = 0.
Journal ArticleDOI
Algorithmic Aspects of Optimal Channel Coding
Siddharth Barman,Omar Fawzi +1 more
TL;DR: In this paper, the authors considered the problem of computing the maximum success probability for a fixed number of messages over a noisy channel with only one use of the channel and showed that it is NP-hard to obtain an approximation ratio strictly better than (1 − e − 1)-approximation.
Journal ArticleDOI
Lower Bounds for Quantum Parameter Estimation
Michael Walter,Joseph M. Renes +1 more
TL;DR: Lower bounds on the size of confidence regions reported by any region estimator for a given ensemble of probe states and probability of success are proved, establishing a general Heisenberg limit for region estimation.
References
More filters
Journal ArticleDOI
A mathematical theory of communication
TL;DR: This final installment of the paper considers the case where the signals or the messages or both are continuously variable, in contrast with the discrete nature assumed until now.
Journal ArticleDOI
An Introduction to Probability Theory and Its Applications
David A. Freedman,William Feller +1 more
An Introduction To Probability Theory And Its Applications
TL;DR: A First Course in Probability (8th ed.) by S. Ross is a lively text that covers the basic ideas of probability theory including those needed in statistics.