1. A stack based tree searching method for the implementation of the List Sphere Decoder ASP-DAC 2006 paper review Presenter : Chun-Hung Lai

2. A stack based tree searching method for the implementation of the List Sphere Decoder 2/20 2015/7/16 Abstract  Maximum likelihood (ML) detection is an optimal solution for the MIMO communication system. List Sphere detector (LSD) is attractive to approach the performance of the ML detector. This paper proposed a VLSI architecture of the tree searching block, which is an essential part of the LSD. The implemented result with 0.25 cell library is 276270 equivalent gates for the 4*4 64QAM. And the area for this design is 3741358 um.

3. A stack based tree searching method for the implementation of the List Sphere Decoder 3/20 2015/7/16 Outline  What’s the problem  Introduction  Introduction and analysis of LSD algorithm  Proposed tree searching architecture for LSD  Conclusions  My comments

4. A stack based tree searching method for the implementation of the List Sphere Decoder 4/20 2015/7/16 What’s the Problem  Existing decoding algorithms for the Maximum likelihood (ML) detection is either high complexity or low efficiency  High complexity are hardly to be implemented Area cost and power consumption are inefficient  So, a practical VLSI architecture with low complexity and high performance becomes the key issues for the lattice decoding point of view

5. A stack based tree searching method for the implementation of the List Sphere Decoder 5/20 2015/7/16 Introduction  Several VLSI architectures are proposed for the ML detection  Sphere Decoder (SD) Computationally efficient, but high complexity  K-best architecture Reduces SD’s high hardware resource usages, but incurs performance degradation  Recently, List Sphere Decoding (LSD) algorithm is proposed  Both low complexity and high performance  This paper proposed  An VLSI architecture of tree searching method used in the LSD

6. A stack based tree searching method for the implementation of the List Sphere Decoder 6/20 2015/7/16 Linear model of MIMO system  The received vector in the MIMO system can be represented y= Hs + n ( H is Nrx * Ntx channel matrix) Nrx: the number of receive antennas Ntx: the number of transmit antennas ( s=[s1 s2 …sNtx] is the Ntx dimensional transmitted signal vector)  The entries of s are chosen from some complex constellation ( n is the additive noise vector)  An optimal method to minimize error of the transmitted signal  Using ML detection at the receiver Q is the set of all possible transmitted vector  Needs an exhaustive search and complexity grow exponentially Ex: In 2*2 MIMO system with 16-QAM modulation 16*16*16*16=65536 transmitted vector need to be considered m …….. (1)

7. A stack based tree searching method for the implementation of the List Sphere Decoder 7/20 2015/7/16 LSD model for the MIMO system  The List Sphere Decoding (LSD) avoids exhaustive search and examining only those points that lie inside a sphere  Using QR factorization of channel matrix H=QU equation (2) can be rewritten to equation (3)  Matrix U is the QR factorized upper-triangular matrix  If the number of transmit antennas is equal to receive antennas …….. (2) …….. (3) Further writing …….. (4) is equal to 0

8. A stack based tree searching method for the implementation of the List Sphere Decoder 8/20 2015/7/16 Operation numbers with no factorization  Operation numbers to select candidates in LSD with equation (1) 1

9. A stack based tree searching method for the implementation of the List Sphere Decoder 9/20 2015/7/16 Operation numbers with factorization  Operation numbers to select candidates in LSD with equation (4)  Multi-stage sequential decoding methodology (4) has smaller operation 4

10. A stack based tree searching method for the implementation of the List Sphere Decoder 10/20 2015/7/16 Operation sequence of LSD algorithm  The following is a 2*2 QPSK example (Nrx=2 and Ntx=2) : Received vector : Candidate vector Chosen from constellation value Number of constellation value is 2

11. A stack based tree searching method for the implementation of the List Sphere Decoder 11/20 2015/7/16 Multi-stage sequential decoding  4 steps in 2*2 QPSK mode  The distance is calculated at each step and compared with r  If the condition is not satisfied, this constellation value which are chosen by s i (entry of candidate vector ) is ignored i=4 for s 4 i=3 for s 3 i=1 for s 1 ….

12. A stack based tree searching method for the implementation of the List Sphere Decoder 12/20 2015/7/16 Operation described by tree searching structure  Tree for the 2*2 QPSK MIMO system  Possible number of constellation value which are chosen by s i are 2  Formal candidate vector = [-0.707 -0.707 -0.707 -0.707] Parallelizable -0.707+0.707

13. A stack based tree searching method for the implementation of the List Sphere Decoder 13/20 2015/7/16 Block diagram of proposed tree searching method  If the calculated distance at the last step is stall smaller than the expected radius, this formal candidate vector is moved to the mem_ctl block 8 parallelized calculation units Each unit calculates the distance of candidates for the specific step

14. A stack based tree searching method for the implementation of the List Sphere Decoder 14/20 2015/7/16 Tree searching sequence in 2*2 QPSK mode  The number in each circle represents the depth and order of the constellation  The latency to select all formal candidate vector Parallelized calculation: 6 Non-parallelized calculation: 12 Non-parallelized calculation Proposed method parallelized calculation Number of formal candidate vector to be selected is equal to 4

15. A stack based tree searching method for the implementation of the List Sphere Decoder 15/20 2015/7/16 Stack operation for tree searching sequence

16. A stack based tree searching method for the implementation of the List Sphere Decoder 16/20 2015/7/16 Accumulated operations in the stack for the worst case  Analyzed for the case of 4*4 64QAM MIMO system  There are 8 constellation values  The calculation step is 2Nrx=2*4=8  Worst case Popped one operation and pushed 8 operations at each step So, the required depth of stack is about 50 Increase 7 at each step

17. A stack based tree searching method for the implementation of the List Sphere Decoder 17/20 2015/7/16 Conclusions  Proposed a stack based tree searching architecture for the LSD algorithm  Two main characteristics Parallelization  Reduced the latency of searching sequence Memory based  Made the design very simple  The implemented codes are synthesized with 0.25 cell library. It has 276270 gates and 3741358 um area.

18. A stack based tree searching method for the implementation of the List Sphere Decoder 18/20 2015/7/16 Grade to my review paper  Excellent good average not-good unacceptable  A. Overall score  B. Overall technical contents  B.1 originality, novelty  B.2 significance of results  B.3 readability  C. Overall presentation  C.1 English usage  C.2 clarity  C.3 adequacy of references  D. Confidence on your decision * * * * * * * * * *

19. A stack based tree searching method for the implementation of the List Sphere Decoder 19/20 2015/7/16 My comments  Low originality  List sphere decoder (LSD) uses multi-stage sequential decoding are proposed by [10]  Illustration and explanation is insufficient  Many figures are ambiguous to understand, however the writer does’t explain in detail  Many errors  Misspell in grammar, index error in formula, index error in chapter  Contribution  This paper is the first one to propose the hardware implementation of LSD algorithm I am inclined to reject this paper

20. A stack based tree searching method for the implementation of the List Sphere Decoder 20/20 2015/7/16 Visualization of the List Sphere Decoding  16 constellation value within 16-QAM modulation  The entry of candidate vector [s1 s2…sNtx] are chosen from those constellation value Constellation value If the distance between the received vector and the candidate vector is less than the expected radius r then this constellation value are really considered by the formal candidate vector Entry of received vector