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Block Interleavers

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Section Overview Block Interleaving Features of the Toolbox Example: Block Interleavers

Section Overview

A block interleaver accepts a set of symbols and rearranges them, without repeating or omitting any of the symbols in the set. The number of symbols in each set is fixed for a given interleaver.

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Block Interleaving Features of the Toolbox

The set of block interleavers in this toolbox includes a general block interleaver as well as several special cases. Each special-case interleaver function uses the same computational code that the general block interleaver function uses, but provides a syntax that is more suitable for the special case. The interleaver functions are described below.

Type of Interleaver	Interleaver Function	Description
General block interleaver	intrlv	Uses the permutation table given explicitly as an input argument.
Algebraic interleaver	algintrlv	Derives a permutation table algebraically, using the Takeshita-Costello or Welch-Costas method. These methods are described in [4].
Helical scan interleaver	helscanintrlv	Fills a matrix with data row by row and then sends the matrix contents to the output in a helical fashion.
Matrix interleaver	matintrlv	Fills a matrix with data elements row by row and then sends the matrix contents to the output column by column.
Random interleaver	randintrlv	Chooses a permutation table randomly using the initial state input that you provide.

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Example: Block Interleavers

The following example illustrates how an interleaver improves the error rate in a communication system whose channel produces a burst of errors. A random interleaver rearranges the bits of numerous codewords before two adjacent codewords are each corrupted by three errors.

Three errors exceed the error-correction capability of the Hamming code. However, the example shows that when the Hamming code is combined with an interleaver, this system is able to recover the original message despite the 6-bit burst of errors. The improvement in performance occurs because the interleaving effectively spreads the errors among different codewords so that the number of errors per codeword is within the error-correction capability of the code.

st1 = 27221; st2 = 4831; % States for random number generator
n = 7; k = 4; % Parameters for Hamming code
msg = randint(k*500,1,2,st1); % Data to encode
code = encode(msg,n,k,'hamming/binary'); % Encoded data
% Create a burst error that will corrupt two adjacent codewords.
errors = zeros(size(code)); errors(n-2:n+3) = [1 1 1 1 1 1];

% With Interleaving
%------------------
inter = randintrlv(code,st2); % Interleave.
inter_err = bitxor(inter,errors); % Include burst error.
deinter = randdeintrlv(inter_err,st2); % Deinterleave.
decoded = decode(deinter,n,k,'hamming/binary'); % Decode.
disp('Number of errors and error rate, with interleaving:');
[number_with,rate_with] = biterr(msg,decoded) % Error statistics

% Without Interleaving
%---------------------
code_err = bitxor(code,errors); % Include burst error.
decoded = decode(code_err,n,k,'hamming/binary'); % Decode.
disp('Number of errors and error rate, without interleaving:');
[number_without,rate_without] = biterr(msg,decoded) % Error statistics

The output from the example follows.

Number of errors and error rate, with interleaving:

number_with =

     0


rate_with =

     0

Number of errors and error rate, without interleaving:

number_without =

     4


rate_without =

    0.0020

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Interleaving

Convolutional Interleavers

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