Variable-length coding (VLC) is a technique used in information theory and data compression to represent symbols with varying numbers of bits based on their frequencies or probabilities of occurrence. The main idea behind VLC is to assign shorter codes to symbols that appear more frequently and longer codes to symbols that appear less frequently, thereby reducing the overall average code length and achieving compression.
The principles of variable-length coding involve:
Huffman Coding: Huffman coding is one of the most common VLC techniques. It constructs a binary tree where each leaf node corresponds to a symbol, and the path from the root to the leaf node represents the code for that symbol. Huffman coding is a prefix-free code, meaning no code is a prefix of another code. The most frequently occurring symbols are closer to the root of the tree, resulting in shorter codes. Less frequent symbols are farther from the root, leading to longer codes.
Arithmetic Coding: Arithmetic coding is another VLC technique that represents sequences of symbols with fractions in the range [0, 1). The entire message is encoded as a single fraction, and the range is subdivided based on the probabilities of symbols. As symbols are processed, the range is updated and narrowed down. The final fraction is then converted into a binary representation.
Variable-length coding finds applications in AC (Alternating Current) signal transmission, particularly in areas like image and audio compression. Here's how VLC is applied in AC signal transmission:
JPEG Compression (Image Compression): In the JPEG (Joint Photographic Experts Group) image compression standard, VLC is used in the quantization and entropy coding stages. After performing the Discrete Cosine Transform (DCT) on image blocks, the resulting coefficients are quantized. The quantized coefficients are then run through a process called Zig-Zag scanning, which rearranges them into a 1D sequence. VLC, often Huffman coding, is then applied to encode the run-lengths of zero coefficients and the non-zero coefficients, taking advantage of the fact that zero runs are usually more frequent. This significantly reduces the amount of data required to represent the image, leading to efficient compression.
MP3 Compression (Audio Compression): In the MP3 audio compression standard, VLC is used to encode the frequency-domain coefficients obtained through the Fast Fourier Transform (FFT). The coefficients are transformed into a perceptual model called the psychoacoustic model, and then quantized and grouped into bands. VLC is applied to the quantized values, with shorter codes assigned to values that contribute more significantly to the perceived audio quality. This helps achieve high compression ratios while maintaining acceptable audio quality.
Variable-length coding is a fundamental technique for achieving data compression, and its applications in AC signal transmission contribute to efficient storage and transmission of multimedia data.