# Channel Coding Rate in the Finite Blocklength Regime

@article{Polyanskiy2010ChannelCR, title={Channel Coding Rate in the Finite Blocklength Regime}, author={Yury Polyanskiy and H. Vincent Poor and Sergio Verd{\'u}}, journal={IEEE Transactions on Information Theory}, year={2010}, volume={56}, pages={2307-2359} }

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…

## 2,388 Citations

### Finite-blocklength channel coding rate under a long-term power constraint

- Computer Science2014 IEEE International Symposium on Information Theory
- 2014

This paper investigates the maximal channel coding rate achievable at a given blocklength n and error probability ε, when the codewords are subject to a long-term power constraint and shows that in both cases the second-order term is proportional to √(log n)/n.

### New channel coding achievability bounds

- Computer Science2008 IEEE International Symposium on Information Theory
- 2008

New upper bounds are given on both average and maximal error probability, which are tighter than existing bounds for many ranges of blocklength and channel parameters of interest, allowing to approximate tightly the maximum rate achievable for a given blocklength.

### Finite blocklength coding for multiple access channels

- Computer Science2012 IEEE International Symposium on Information Theory Proceedings
- 2012

This paper studies the maximum achievable rate region of multiple access channels (MAC) for a given blocklength n and a desired error probability ϵ and provides general converse bounds for both average error probability and maximum error probability criteria.

### Block-Fading Channels at Finite Blocklength

- Computer ScienceISWCS
- 2013

This tutorial paper deals with the problem of characterizing the maximal achievable rate R* ( n ,e) at a given
blocklength n ; and error probability e over block-fading channels. We review recent…

### Finite Blocklength Rates over a Fading Channel with CSIT and CSIR

- Computer Science2018 IEEE International Conference on Communications (ICC)
- 2018

Lower and upper bounds are obtained on the maximal transmission rate at a given codeword length $n$ and the rate enhancement possible due to the channel state information at the transmitter in the finite blocklength regime.

### Finite-blocklength bounds on the maximum coding rate of rician fading channels with applications to pilot-assisted transmission

- Computer Science2017 IEEE 18th International Workshop on Signal Processing Advances in Wireless Communications (SPAWC)
- 2017

Borders are presented on the maximum coding rate achievable over a Rician block-fading channel for a fixed packet size and a fixed packets error probability to quantify the tradeoff between the rate gains and rate loss resulting from fast channel variations and pilot-symbol overhead.

### Finite Blocklength Information Theory: What Is the Practical Impact on Wireless Communications?

- Computer Science2016 IEEE Globecom Workshops (GC Wkshps)
- 2016

The true outage probability in Ricean and Nakagami-m block fading channels is investigated and it is proved that the asymptotic outage capacity is the Laplace approximation of the average error probability in finite blocklength regime.

### Quasi-static SIMO fading channels at finite blocklength

- Computer Science2013 IEEE International Symposium on Information Theory
- 2013

It is shown that the channel dispersion is zero regardless of whether the fading realizations are available at the transmitter and/or the receiver, and it is verified that, in some scenarios, zero dispersion indeed entails fast convergence to outage capacity as the blocklength increases.

### Learning Channel Codes from Data: Performance Guarantees in the Finite Blocklength Regime

- Computer Science
- 2023

It is shown analytically that the asymptotic expansion of the bounds for the maximum achievable code rate of the learning-based channel codes are tight for sufficiently large training data.

### On the second-order coding rate of non-ergodic fading channels

- Computer Science2013 51st Annual Allerton Conference on Communication, Control, and Computing (Allerton)
- 2013

This paper analyzes the rate-reliability trade-off for non-ergodic fading channels with state information available at the receiver, specifically the second-order coding rate with a fixed length…

## 58 References

### New channel coding achievability bounds

- Computer Science2008 IEEE International Symposium on Information Theory
- 2008

New upper bounds are given on both average and maximal error probability, which are tighter than existing bounds for many ranges of blocklength and channel parameters of interest, allowing to approximate tightly the maximum rate achievable for a given blocklength.

### Lower Bounds to Error Probability for Coding on Discrete Memoryless Channels. I

- Computer Science
- 1993

The paper is presented in two parts: the first, appearing here, summarizes the major results and treats the case of high transmission rates in detail; the second, to appear in the subsequent issue, treats the cases of low transmission rates.

### Lower Bounds to Error Probability for Coding on Discrete Memoryless Channels. II

- Computer ScienceInf. Control.
- 1967

### A simple derivation of the coding theorem and some applications

- Computer ScienceIEEE Trans. Inf. Theory
- 1965

Both amplitude-discrete and amplitude-continuous channels are treated, both with and without input constraints, and the exponential behavior of the bounds with block length is the best known for all transmission rates between 0 and capacity.

### Simple channel coding bounds

- Computer Science2009 IEEE International Symposium on Information Theory
- 2009

New channel coding converse and achievability bounds are derived for a single use of an arbitrary channel using a quantity called the “smooth 0-divergence”, which is a generalization of Rényi's divergence of order 0.

### Probability of error for optimal codes in a Gaussian channel

- Computer Science
- 1959

Upper and lower bounds are found for the error probability in decoding with optimal codes and decoding systems for a continuous channel with an additive gaussian noise and subject to an average power limitation at the transmitter.

### A Study on Universal Codes With Finite Block Lengths

- Computer ScienceIEEE Transactions on Information Theory
- 2007

Simulation results show that universal performance can be a practical goal as the block lengths become large, and an alternative proof of Root and Varaiya's compound channel coding theorem for linear Gaussian channels is presented.

### Information Spectrum Approach to Second-Order Coding Rate in Channel Coding

- Computer ScienceIEEE Transactions on Information Theory
- 2009

The optimum second-order transmission rate with a constant error constraint epsiv is obtained by using the information spectrum method and it is clarified that the Gallager bound does not give the optimum evaluation in the second- order coding rate.

### A general formula for channel capacity

- Computer ScienceIEEE Trans. Inf. Theory
- 1994

A formula for the capacity of arbitrary single-user channels without feedback is proved and capacity is shown to equal the supremum, over all input processes, of the input-output inf-information rate defined as the liminf in probability of the normalized information density.