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LNS Arithmetic for MPEG Encoding Using a Fast DCT

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

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  1. LNS Arithmetic for MPEG Encoding Using a Fast DCT Jie Ruan and Mark G. Arnold

  2. 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)

  3. 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.

  4. Multiplication Logb(XY)=logbX+logbY The cost is a fixed-point adder Addition 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

  5. Major parts of MPEG Encoding • RGBYUV • Motion Estimation • Discrete Cosine Transform (DCT) • Variable Length Coding

  6. 2-D Discrete Cosine Transform 2 Dimensional 8x8 DCT

  7. 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.

  8. 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

  9. Numerical results (SNR)

  10. 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

  11. Compares LNS DCT with Fixed-point DCT Comparison Hardware cost for Chen’s algorithm, at F=4

  12. Conclusion • 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

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