1. ECE 734 S13 EST. 1891 University of Wisconsin-Madison BIT MATRIX TRANSPOSE WITH TENSOR PRODUCT AND PERFECT SHUFFLING FOR SOFTWARE DEFINED RADIO ECE 734 VLSI Array Structures for Digital Signal Processing Jui-Chieh (Jerry) Lin University of Wisconsin-Madison May. 8 th, 2013

2. EST. 1891 ECE 734 S13 Jui-Chieh Lin University of Wisconsin-Madison Bit Matrix Transpose What is bit matrix transpose? Transpose the matrix in which each element is one bit Application of bit matrix transpose Interleaver in software defined radio Helps combat burst error in forward error correction Not so efficient on word-based processor A word is a register performs parallel bit-operations together Inherent mismatch on data format Slide 2

3. EST. 1891 ECE 734 S13 Jui-Chieh Lin University of Wisconsin-Madison Related Work: Bit Operations on Processor is NOT Easy Bit tricks Using bit level manipulation tricks Limited applications and high engineering overhead b = ((b * 0x0802 & 0x22110) | (b * 0x8020 & 0x88440)) * 0x10101 >> 16; // reverse a byte in an integer b Look up table Store bits positions, i.e. pattern, in memory and look up Expensive memory storage (a few bytes per bit location) Wifi 288 bits interleaver needs 288 of 9-bit-entries LTE-Advanced 6144 bit interleaver needs 6144 13bit-entries Slide 3

4. EST. 1891 ECE 734 S13 Jui-Chieh Lin University of Wisconsin-Madison Perfect Shuffling in Modern Processors Perfect shuffling operator S m,n Transpose m×n matrix to n×m matrix Perfect shuffling (S 16,2 ) on Texas Instruments C64

5. EST. 1891 ECE 734 S13 Jui-Chieh Lin University of Wisconsin-Madison Tensor Product: Proposed Framework for Bit Matrix Transpose

6. EST. 1891 ECE 734 S13 Jui-Chieh Lin University of Wisconsin-Madison Matrix Transpose Implementation

7. EST. 1891 ECE 734 S13 Jui-Chieh Lin University of Wisconsin-Madison Preliminary Results (Square Bit Matrix Transpose) Algorithm transformation of Bit Matrix Transpose Bit parallel algorithms perform over 9X cycle reduction Slide 7 Around 10x

8. EST. 1891 ECE 734 S13 Jui-Chieh Lin University of Wisconsin-Madison Summary Slide 8 Bit matrix transpose 9x speed up comparing to naïve method on Texas Instruments' C64x Future work Rectangular bit-matrix transpose

9. ECE 734 S13 EST. 1891 University of Wisconsin-Madison Questions? Slide 9