1. Variable Length LDPC Codes for 45GHz
Date:
Authors:
Name
Affiliations
Address
Phone
Yan Li
Gigaray Communication
Wuxi China
Feng Huang

2. Quasi-cyclic low density parity check codes
A QC-LDPC is defined by a J-by-L base matrix and the size of sub-matrices, p.
A J-by-L base matrix has the following representation. (0<=i<J, 0<=i<L) represents a p-by-p sub-matrix: 0 represents an identity matrix; -1 represents a zero matrix; other non-zero less-than-p values represent circulant permutation matrices.

3. Considerations
LDPC codes proposed in [1] has been adopted by draft standard.
Compared to other semi-static wireless channels, indoor mmw communication channel has more variations because of rich reflections/scattering and moving objects. It is desirable for receiver to have more adaptation to channel variation.
Besides code rate, code length provides another dimension of coding gain change, thus improves the receiver’s adaptation capability to channel variations
It is desirable to be compatible to existing coding scheme and minimize the added complexity.

4. LDPC Base matrices (1) Same base matrices proposed by ZTE in [1].
Four code rates are 1/2, 5/8, 3/4 and 13/16.
Rate 1/2：
Rate 5/8： -1  0 34 12 36 18  8 13 16 40 32 22 19 20  2 28 21 30 14 37 31 38  6 26 24 10  5 -1  0 32 22 18 19  8 16 40 34 12 36 21 30 20 38  6 13 31 24  2 28 37 10 14  5

5. LDPC Base Matrices (2) Rate 3/4： Rate 13/16： 0 -1 8 16 40 34 32 12 22 0 -1  8 16 40 34 32 12 22 36 18 13 19 30 20 38  2  6 28 37 26 21 31 24 10 14 5  0 -1 30 20 18 22 38  2  6 28 32 37 26 21 34 40 24 12 10 14 16 19  8 13  5

6. Variable LDPC code length
Based on the sets of base matrices by [1], code length change is achieved by changing p , the sub-matrix size.
p=42 maintains the same set of 672 long LDPC codes proposed by ZTE.
(672 , 366), (672 , 420), (672 , 504) and (672, 546) codes
p=126 introduces a set of LDPC codes with code length of 2016.
(2016, 1008), (2016, 1260), (2016, 1512) and (2016, 1638) codes
1-bit signaling field to indicate the code length

7. Performance of rate ½ codes (1)
QPSK modulation and AWGN

8. Performance of rate ½ codes (2)
16QAM modulation and AWGN

9. Performance of rate ½ codes (3)
64QAM modulation and AWGN

10. Performance of rate 5/8 codes(1)
QPSK modulation and AWGN

11. Performance of rate 5/8 codes(2)
16QAM modulation and AWGN

12. Performance of rate 5/8 codes(3)
64QAM modulation and AWGN

13. Performance of rate 3/4 codes(1)
QPSK modulation and AWGN

14. Performance of rate 3/4 codes(2)
16QAM modulation and AWGN

15. Performance of rate 3/4 codes(3)
64QAM modulation and AWGN

16. Performance of rate 13/16 codes(1)
QPSK modulation and AWGN

17. Performance of rate 13/16 codes(2)
16QAM modulation and AWGN

18. Performance of rate 13/16 codes(3)
64QAM modulation and AWGN

19. Benefits of proposed scheme
All benefits from base matrices proposed in [1] are maintained.
Improved performance of 0.1dB ~ 0.8dB achieved by longer codes compared to short codes.
This also means finer coding gain grids for finer ACM adaptation.
The short codes and long codes can share the same encoder and decoder.
For decoder, larger value of p implies possible higher parallel processing, thus higher throughput, although at the expense of more logic and memory in ASIC implementation.

20. Complexity Encoding, compared to the short codes in [1]
For long codes, buffer size needs to be tripled.
Because the base matrices are the same, logic resources won't be increased if tripling of latency is tolerable, or logic resouces need to be tripled to maintain the same latency.
Decoding, compared to the short codes in [1]
For layered decoding, logic resources for variable and check node processing won't be increased if throughput keeps the same. However, the shifting network complexity will increase.
For full parallel implementation, the logic resources will be tripled.

21. Conclusion
Variable LDPC code length is proposed to improved performance and channel adaptation capability.
Compatible to existing LDPC codes [1] adopted by the standard draft.
No need to add new encoder and decoder

22. References
[1]. LDPC Coding for 45GHz( aj). Proposal of IEEE802.11aj(45G).