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 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
• 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.
Multiplication

Logb(XY)=logbX+logbY

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)

Logb(X+Y)=y+sb(z)

LNS Arithmetic Units
Major parts of MPEG Encoding
• RGBYUV
• Motion Estimation
• Discrete Cosine Transform (DCT)
• Variable Length Coding
2-D Discrete Cosine Transform

2 Dimensional 8x8 DCT

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
• At F=4, a visually acceptable precision

10-bit LNS

16-bit Fixed-point

64-bit Floating-point

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