Lns arithmetic for mpeg encoding using a fast dct
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LNS Arithmetic for MPEG Encoding Using a Fast DCT. Jie Ruan and Mark G. Arnold. LNS (Logarithmic Number System). Represents a number by a sign bit and an exponent to a certain base (b). S. Exponent (n-1 bits). F (Precision). Properties of LNS. Large dynamic range

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Lns logarithmic number system l.jpg
LNS (Logarithmic Number System)

  • Represents a number by a sign bit and an exponent to a certain base (b)


Exponent (n-1 bits)

F (Precision)

Properties of lns l.jpg
Properties of LNS

  • Large dynamic range

  • Easy for multiplications, divisions and exponentiations

  • Additions are not linear operations for LNS

  • Cost of adders is exponential to word length

  • Has advantages at low precisions.

Lns arithmetic units l.jpg



The cost is a fixed-point adder


More complex process than multiplication

E.g., when calculating logb(X+Y), (x=logbX, y=logbY)

Calculate z=x-y

Table-lookup sb(z)=logb(1+2z)


LNS Arithmetic Units

Major parts of mpeg encoding l.jpg
Major parts of MPEG Encoding


  • Motion Estimation

  • Discrete Cosine Transform (DCT)

  • Variable Length Coding

2 d discrete cosine transform l.jpg
2-D Discrete Cosine Transform

2 Dimensional 8x8 DCT

Berkeley mpeg encoder l.jpg
Berkeley MPEG Encoder

  • Berkeley MPEG Tool is a software to perform MPEG encoding and decoding, written in C language.

  • The DCT function is modified to accommodate LNS features.

Visual effect of mpeg encoding with lns dct l.jpg
Visual Effect of MPEG Encoding with LNS DCT

  • At F=4, a visually acceptable precision

10-bit LNS

16-bit Fixed-point

64-bit Floating-point

Hardware implementation for dct l.jpg
Hardware implementation for DCT

  • NxN 2 Dimensional DCT

    • Usually performed through 2 rounds of 1-D N-point DCT, with an NxN buffer

    • Less hardware and simpler data input arrangement than direct 2-D implementations

  • Chen’s 1-D DCT algorithm

    • Directly factorizes the DCT matrix

    • 16 multiplications

    • 26 additions

Compares lns dct with fixed point dct l.jpg
Compares LNS DCT with Fixed-point DCT

Comparison Hardware cost for Chen’s algorithm, at F=4

Conclusion l.jpg

  • At low precisions LNS is a good way for DCT in MPEG, compared to Fixed-point

    • shorter word length

    • less area

    • Comparable visual result

  • LNS is a good alternative for MPEG encoding