Finite Block Length Regime

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Hello,

Anyone can help us to show how to calcuate Finite Block Length Regime rate in matlab please.

Thanks

Answer 1

[Arjun]

Hi @A_SD,

I see that you need help in calculating Finite Block Length Regime Rate using MATLAB code.

The finite block length regime refers to the performance analysis of communication systems when the block length is not asymptotically large. Calculating the finite block length regime rate involves using the normal approximation to the channel coding theorem. This typically involves parameters like block length (n), error probability (epsilon), and channel capacity (C).

Kindly refer to the following code for implementation details:

% Parameters
n = 1000;  % Block length
epsilon = 1e-3;  % Error probability
C = 1;  % Channel capacity (bits per channel use)
V = 1;  % Channel dispersion (depends on the channel, e.g., BSC or AWGN)

% Q-function (Gaussian tail probability)
Q = @(x) 0.5 * erfc(x / sqrt(2));

% Calculate the inverse Q-function using MATLAB's qfuncinv
Q_inv = @(x) sqrt(2) * erfcinv(2 * x);

% Calculate the finite block length rate using the normal approximation
rate = C - sqrt(V/n) * Q_inv(epsilon);

% Display the result
fprintf('Finite Block Length Regime Rate: %.4f bits/channel use\n', rate);

I hope this will help!

Answer 2

[Ruchika]

Hello @A_SD,

I would be happy to help you with the calculation of the finite block length regime rate. This involves understanding the relationship between block length, error probability, and channel capacity in the finite block length regime of information theory.

To get started, we can use the normal approximation for the maximum coding rate ( R ) given by:

[ R \approx C - \sqrt{\frac{V}{n}} Q^{-1}(\epsilon) ]

where:

• ( C ) is the channel capacity.
• ( V ) is the channel dispersion.
• ( Q^{-1} ) is the inverse of the Q-function, which represents the tail probability of the standard normal distribution.

Here's a simple MATLAB script you can use to perform this calculation:

% Define parameters
C = 1; % Channel capacity (example value)
V = 1; % Channel dispersion (example value)
n = 100; % Block length
epsilon = 1e-3; % Error probability

% Q-function inverse (using the complementary error function)
Q_inv = @(x) sqrt(2) * erfcinv(2 * x);

% Calculate finite block length rate
R = C - sqrt(V / n) * Q_inv(epsilon);

% Display result
fprintf('Finite Block Length Regime Rate: %.4f\n', R);

Explanation:

• Channel Capacity (C): This is the theoretical maximum rate at which information can be reliably transmitted over the channel.
• Channel Dispersion (V): This quantifies the variability in the channel's capacity due to noise and other factors.
• Block Length (n): Represents the length of the codewords you're using.
• Error Probability (ε): The likelihood of a decoding error occurring.

Hope this helps!