1. Fixed point Software Implementation of a
Low-Complexity Soft Demapper
Presented By : Adeel Akhtar
Supervised By : Imran Ali
Presented To : Prof. Norbert Wehn
Microelectronics Seminar

2. Outline
 Introduction
 Goals
 Work Description
 Simulation Results
 Conclusion
2

3. Channel
Encoder
Channel
Mapper
Demapper
Channel
Decoder
The received symbols are mapped to soft values:
0.7,-1.3,-0.1,1.4; 3.1, -0.7, -1.1, 2.3
Error correction data is added to the message:
01100110
The soft values are used to recover the original
message: 1011
Message to be sent: 1011
The message is mapped to symbols
describing the signal.
(-1+2i, -1+2i)
Sending the signal through the channel distorts it.
(-0.76+1.3i; -1.1+2.15i)
Wireless Communication
3

4. Channel
Encoder
Channel
Mapper
Demapper
Channel
Decoder
Im
Re
0111 0110
01000101
0010 0011
00010000
1000 1001
10111010
1101 1100
11101111
Due to interference the sent signal is
deformed.
Wireless Channel
4

5. 1.Optimal Soft Demapper
Channel
Encoder
Channel
Mapper
Demapper
Channel
Decoder





 





 





0
2
1
0
0
2
||
exp
||
exp
log
N
xy
N
xy
LLR
i
i
Sx
Sx
i
Im
Re
0111 0110
01000101
0010 0011
00010000
1000 1001
10111010
1101 1100
11101111
Demapper Algorithms
5

6. Channel
Encoder
Channel
Mapper
Demapper
Channel
Decoder
Im
Re
0111 0110
01000101
0010 0011
00010000
1000 1001
10111010
1101 1100
11101111
2.Sub-optimal Demapper
0
2
0
2
1
||min||min
N
xyxy
LLR ii SxSx
i



6

7. Channel
Encoder
Channel
Mapper
Demapper
Channel
Decoder
0
2
0min
2
1min ||||
N
xyxy
LLR ii
i


3.Less Complex Sub-Optimal Soft Demapper [1]
Im
Re
0111 0110
01000101
0010 0011
00010000
1000 1001
10111010
1101 1100
11101111
7

8.  Fixed point software implementation of the
algorithm in C++.
 Simulation of the demapper with Duo binary
Turbo Decoder.
 Communication performance analysis with
different bit widths and comparison with
Optimal technique.
8
Goals of Seminar

9. Block Diagram of Algorithm
9
Received Symbol
Real Img
Rounding
Distance
Calculation
Magnitude to Gray Code
Closest flipped bit
constellation point
Gray Code to Magnitude
Calculation of Log Likelihood Ratio (LLRs)
(-2.7,1.4)
(-3,1)
(1001)
10010011
10011101
10011011
10011000
0011( 1, 1)
1101(-3,-1)
1011(-1, 1)
1000(-3, 3)
llro = -72.3
llr1 = 29.9
llr2 = 15.9
llr3 = -10.4

10. Closest flipped bit constellation points
 Flipping the bit at needed position.
…xxxxxxxxx…  ...x’x1x0x0x0…
 The next less significant bit is set.
 All lesser significant bits are reset.
 Real and imaginary numbers are interleaved.
10
Example: symbol with four bits (1001)
Flip bit 0: xxxx → x’x1x (10010011)
Flip bit 1: xxxx → xx’x1 (10011101)
Flip bit 2: xxxx → xxx’x (10011011)
Flip bit 3: xxxx → xxxx’ (10011000)

11. Fixed-Point Low-Complexity Soft Demapper
11
Received Symbol
Real Img
Rounding
Distance
Calculation
Magnitude to Gray Code
Closest flipped bit
constellation point
Gray Code to Magnitude
Calculation of Log Likelihood Ratio (LLRs)
(-906,485)
(-971,323)
(1001)
10010011
10011101
10011011
10011000
0011( 323, 323)
1101(-971,-323)
1011(-971, 323)
1000(-971, 971)
llro = -13
llr1 = 30
llr2 = 16
llr3 = -10
Fixed point number Q.10,8

12. Simulation Setup
12
Source
Statistics
Turbo encoder 16 QAM Mapper
16 QAM
De-Mapper
Turbo
Decoder
Transmitter (Tx)
Receiver(Rx)
Channel

13. Simulation Results
13
6 6.2 6.4 6.6 6.8 7 7.2
10
-5
10
-4
10
-3
10
-2
10
-1
10
0
SNR Eb/N0 dB
FER
Info bits1552 total bits1864-16QAM R0.833 Turbo Decoder
Optimal Demapper

14. Simulation Results
14
6 6.2 6.4 6.6 6.8 7 7.2
10
-5
10
-4
10
-3
10
-2
10
-1
10
0
SNR Eb/N0 dB
FER
Info bits1552 total bits1864-16QAM R0.833 Turbo Decoder
Optimal Demapper
Proposed. Q10,8

15. Simulation Results
15
6 6.2 6.4 6.6 6.8 7 7.2
10
-5
10
-4
10
-3
10
-2
10
-1
10
0
SNR Eb/N0 dB
FER
Info bits1552 total bits1864-16QAM R0.833 Turbo Decoder
Optimal Demapper
Proposed. Q10,8
Proposed. Q8,6

16. Conclusions
1. Understanding of a less complexity sub-optimal
demapper.
2. Fixed point software implementation of the proposed
algorithm.
3. The performance of the algorithm is exactly similar
to the optimal algorithm for 16 QAM.
4. Less number of distances computation,
consequently less computation complexity in
hardware.
16

17. 17
Thank You