Detailed explanation of interweaving technology

This column contains the core knowledge of information theory and coding, organized by knowledge points, and can be used as a reference for teaching or learning. The markdown version has been archived to [Github repository: https://github.com/timerring/information-theory ] or public account [AIShareLab] to reply to Information Theory .

interleaving technology

1. Burst error

• Interference, fading, equalization, etc. will all introduce burst errors.
• After channel coding and decoding, the errors of its decoding output will also appear bursty, whether it is a block code or a convolutional code.
  • Threshold Effect of Channel Coding and Decoding

Convolutional codes have poor burst error resistance

• Convolutional codes are protected by the correlation between adjacent symbols, and the maintenance time of this correlation is generally short
• The error correction ability of block codes to burst errors and random errors is basically the same, but the code length is shorter, and the bursts that are slightly longer are powerless
• There are also block codes specially designed for burst errors, but the ability to correct random errors is correspondingly reduced

2. An effective means of resisting sudden errors - interweaving

Interleaving (interleaving) is a processing method that transforms the order of the data sequence. Also known as permutation.

General representation of an interleaver

• Interleaving table: $\mathbf{j}=T\left(i\right)$, means that the j-th symbol of the output sequence is taken from the i-th symbol of the input sequence. That is, when the input sequence is$x_1,x_2,\dots$ , the output sequence is$y_1,y_2,When\; ...$ , $ y_{j}=x_{T(i)}$.

3. Three important parameters of the interleaver

• interleaving delay
• The minimum distance between adjacent symbols before interleaving is called interleaving depth
• The minimum distance between adjacent symbols after interleaving is called the interleaving width

Basic interleaving (block interleaving, block interleaver)

Divide the data stream into lengths $\mathbf{W}\ast block\; of\; L$ , write data line by line to a$L$行$The\; matrix-shaped\; buffer\; of\; W$ columns is filled and then read out column by column.

The depth is $L$ , with width$W$ , the delay is$WL$ . The sum of the delays of interleaving and deinterleaving is 2WL.

The input sequence is $x_1,x_2,\dots ,x_{RC}$; The output sequence is $y_1,y_2,\dots ,y_{RC}$ 。

Summarize

• Convolutional Codes: Concepts, Coding, Connected Vectors, State Diagrams, Trellis Diagrams, Viterbi Decoding Algorithms.
• Interleaving Technology: Resistance to Burst Errors

Channel coding summary:

• Block codes (n, k), cyclic codes - memoryless codes
• Convolutional code (n, k, L) - with memory coding

references:

1. Proakis, John G., et al. Communication systems engineering. Vol. 2. New Jersey: Prentice Hall, 1994.
2. Proakis, John G., et al. SOLUTIONS MANUAL Communication Systems Engineering. Vol. 2. New Jersey: Prentice Hall, 1994.
3. Zhou Jiongpan. Communication Principles (3rd Edition) [M]. Beijing: Beijing University of Posts and Telecommunications Press, 2008.
4. Fan Changxin, Cao Lina. Principles of Communication (7th Edition) [M]. Beijing: National Defense Industry Press, 2012.