# A-law algorithm

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Graph of μ-law & A-law algorithms

An A-law algorithm is a standard companding algorithm, used in European 8-bit PCM digital communications systems to optimize, i.e., modify, the dynamic range of an analog signal for digitizing. It is one of two versions of the G.711 standard from ITU-T, the other version being the similar µ-law, used in North America and Japan.

For a given input x, the equation for A-law encoding is as follows,

where A is the compression parameter. In Europe, .

A-law expansion is given by the inverse function,

The reason for this encoding is that the wide dynamic range of speech does not lend itself well to efficient linear digital encoding. A-law encoding effectively reduces the dynamic range of the signal, thereby increasing the coding efficiency and resulting in a signal-to-distortion ratio that is superior to that obtained by linear encoding for a given number of bits.

## Comparison to μ-law[edit]

The μ-law algorithm provides a greater larger dynamic range than the A-law at the cost of worse proportional distortion for small signals. By convention, A-law is used for an international connection if at least one country uses it.

## See also[edit]

- μ-law algorithm
- Audio level compression
- Signal compression
- Companding
- G.711
- DS0

## External links[edit]

- Waveform Coding Techniques - Has details of implementation (but note that the A-law equation is incorrect)
- A-Law and μ-law Companding Implementations Using the TMS320C54x (PDF)
- A-law implementation in C-language with example code

[hide] Data compression methods
Lossless |
Entropy type | Unary Arithmetic Golomb Huffman Adaptive Canonical Modified Range Shannon Shannon–Fano Shannon–Fano–Elias Tunstall Universal Exp-Golomb Fibonacci Gamma Levenshtein
Dictionary type | Byte pair encoding DEFLATE Lempel–Ziv LZ77 / LZ78 (LZ1 / LZ2) LZJB LZMA LZO LZRW LZS LZSS LZW LZWL LZX LZ4 Statistical
Other types | BWT CTW Delta DMC MTF PAQ PPM RLE
Audio |
Concepts | Bit rate average (ABR) constant (CBR) variable (VBR) Companding Convolution Dynamic range Latency Nyquist–Shannon theorem Sampling Sound quality Speech coding Sub-band coding
Codec parts | A-law μ-law ACELP ADPCM CELP DPCM Fourier transform LPC LAR LSP MDCT Psychoacoustic model WLPC
Image |
Concepts | Chroma subsampling Coding tree unit Color space Compression artifact Image resolution Macroblock Pixel PSNR Quantization Standard test image
Methods | Chain code DCT EZW Fractal KLT LP RLE SPIHT Wavelet
Video |
Concepts | Bit rate average (ABR) constant (CBR) variable (VBR) Display resolution Frame Frame rate Frame types Interlace Video characteristics Video quality
Codec parts | Lapped transform DCT Deblocking filter Motion compensation
Theory | Entropy Kolmogorov complexity Lossy Quantization Rate–distortion Redundancy Timeline of information theory
Compression formats Compression software (codecs)

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