Powerful Error Correcting Codes

1
Powerful Error Correcting Codes for Optical
Communication Systems and Spread Spectrum Systems
??????????????????? ???????????????????
Chen Zheng ? ?
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2
Contents
Background and Motivation (Chap.1,2)?????
Contributions
Turbo Decoding for Hard-Detected Signals (Chap.3)
????????????????
Decoding of Low-Density Parity-Check Codes
for Hard-Detected Signals (Chap.4) ???????????????
??????????
Chip-by-Chip Turbo Coding for Direct-Sequence Spre
ad-Spectrum Systems (Chap.5) ?????????????????????
??????
Conclusions (Chap.6)???
3
Performance of Powerful Codes

• The performance of error correcting codes is
• bounded by the Shannon s limit.

Powerful codes result in near Shannons
limit performance.
Turbo Codes
Low-Density Parity-Check Codes
4
Powerful Error Correcting Codes
Turbo Codes

• The whole code is the concatenation of
• interleaved component codes.

LDPC (Low-Density Parity-Check) Codes

• The whole code is equal to the intersection of
• interleaved component parity-check codes.

• There are two important items of both codes

• Iterative decoding using soft values

• Large interleaving size (Long data block)

Introduction of powerful decoding method with a
brief example of a turbo code
5
(1) Code Structure
Turbo encoder
Turbo decoder
info. bits
Decoder 1
?
Encoder 1
?
channel
?
-1
Decoder 2
?
Encoder 2
-1
?
?
Interleaver
De-Interleaver

• Concatenated component encoders and
• corresponded decoders

• Interleaver between component codes

For different versions of the same information
sequence
6
(2) Decoding with Soft Values
channel output
Turbo encoder
Turbo decoder
info. bits
Decoder 1
?
Encoder 1
?
channel
?
-1
Decoder 2
?
Encoder 2
-1
?
?
Interleaver
De-Interleaver

• Using soft-decision decoding algorithms with
• soft values rather than hard-decision
• Soft-decision consisting of more reliable
  information
• Hard-decision no reliable information

7
(3) Iterative Decoding
Turbo encoder
Turbo decoder
info. bits
Decoder 1
?
Encoder 1
?
channel
?
-1
Decoder 2
?
Encoder 2
-1
?
?
Interleaver
De-Interleaver
decisions

• Passing soft values from the output of one
• decoder to the input of the other decoder

• To iterate (repeat) this process several times
• to produce more reliable decisions

8
(4) Interleaving Effect
Turbo encoder
Turbo decoder
info. bits
Decoder 1
?
Encoder 1
?
channel
?
-1
Decoder 2
?
Encoder 2
-1
?
?
Interleaver
De-Interleaver

• To allow the component decoders making randomly
• independent estimates of the soft values of
  the
• same information bit
• Large interleaving size resulting in less
  correlated
• estimates and better effect of iterative
  decoding

9
Two Important Items of Powerful Codes
BER
soft-decision decoding
10-1

• Soft values are required
• for the performance
• improvement.

10-2
hard-decision decoding
10-3
10-4
10-5
0
Eb/No dB
1
2
3
4
BER

• Large interleaving
• size (longer block
• length) is required
• for the performance
• improvement.

long block 10000 bits
10-1
10-2
short block 100 bits
10-3
10-4
10-5
0
Eb/No dB
1
2
3
4
10
Limitation of Using Soft Values

• There are communication systems with
• requirement of the hard-detected signals.
• It is difficult to realize the soft-detection
  process.

or

• An example
• Optical Fiber Communication (OFC) Systems

Decoding with soft values may be unrealizable.
11
OFC Systems

• High transmitting data speed

• Compensation of optical loss

optical amplifiers

• Erbium-doped fiber amplifier (EDFA)

• Amplifier spontaneous emission (ASE) noise

• Degradation of signal-to-noise-ratio

E/O
ASE noise grows proportionally with the number of
amplifiers.
amplifier
O/E

• Error Correcting Codes against ASE noise

12
Limitation for OFC Systems

• Hard detection is a mainly used detection
• scheme for OFC systems.

• Much high transmission data rate

• No optical/electrical converter to realize soft
• detection for OFC systems

• Decoding schemes with powerful soft-decision
• decoding may be impossible.

13
Motivations of Research (1)
Using error detection process to
convert hard-decision to soft value
Combining powerful error correcting
decoding schemes with such soft value

• Turbo codes

Concatenation of error detector

• LDPC codes

Using error detection process in the code
structure directly
14
Limitation of Realization of Large Interleaving
Size

• There are communication systems with requirement
• of short transmission data block.

• An example packet communication for
• wireless communication
  systems

• Short transmission data block may be required.

• Large interleaving size may be unrealizable.

15
Motivations of Research (2)
Using spread-spectrum techniques to achieve large
interleaving size
In DS/SS systems, a spreading sequence spreads an
information bit into many chips.
Turbo Codes for DS/SS Systems
First Turbo encoding, then DS spreading
Spreading sequence
Bit-by-Bit Turbo Encoder
Bit level
Bit level
Chip sequence
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Proposed Chip-by-Chip Turbo Coding

• Spreading input bit using spreading sequence

• Turbo coding and decoding in chip-timing

Spreading sequence
chip sequence
NK chips
Chip-by-Chip Turbo Encoder
K bits
Bit level
Chip level
chip size N
interleaving size NK
Results Large interleaving size with
short block length for turbo codes
17
Contributions
Turbo Decoding for Hard-Detected Signals, i.e.
Optical Fiber Communication Systems (Chap.3)
Decoding of LDPC Codes for Hard-Detected
Signals, i.e. Optical Fiber Communication
Systems (Chap.4)
Chip-by-Chip Turbo Coding Scheme for
Direct- Sequence Spread-Spectrum Systems (Chap.5)
This part will not be further presented
18
Part 1
Turbo Decoding for Hard-Detected Signals, i.e.
Optical Fiber Communication Systems (Chap.3)
Part 2
Decoding of LDPC Codes for Hard-Detected Signals,
i.e. Optical Fiber Communication Systems (Chap.4)
19
Motivation of Research

• Converting hard-detected signals into soft
• values

• Combining soft-decision decoding of powerful
• codes with such reliability

Error detection is used for converting hard-decisi
on to soft value.
Error detecting encoder
Binary-in Binary-out Channel
hard
soft
Error detector
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Converting Hard-Decision into Soft Value

• The channel outputs are hard-detected binary
• values as 1 or 1.

• It is impossible to obtain reliable information
  from
• a single data bit.

• For a data block, the error detection can be
  used
• to know the situation of all bits in a block
• whether consisting errors or not.

• The error detection can provide reliable
  information
• to all bits in a block.

21
Reliability based on Error Detection
encoding by error- detecting code
1 0 1 1
1
parity-check bit
error detecting
1 0 1 1 1
without error
1 0 0 1 1
with error

• good state a block w/o detected error

• bad state a block with detected error

• Converting hard-decision into two-level
  reliability for

good state
bad state
and
22
Proposed System Model
Error detecting encoder

Turbo encoder
Inter- lever






OFC channel


hard
soft
Turbo decoder
De-Inter- lever


Reliability decision



error-detection
23
Decision of Error-Detected Reliability
0 0 1 1 1 1 1 0 0 0 1 1
code block
interleaved
0 1 1 0 0 1 0 1 1 1 0 1
0 1 1 0 0 0 1 0 1 0 1 1 0 1 1
parity-check encoding
corrupted by error
0 1 1 0 0 0 0 0 1 0 1 1 0 1 1
01 1-1
0 1 1 0 0 0 0 1 1 1 0 1
error detection good and bad state
g g g g b b b b g g g g
de-interleaved
g -b -g g b g g -b -g -g b -g
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Proposed Scheme for Simulation

• In proposed decoding

Error-detected reliability instead of soft
values with known channel state information

• Error-detecting code

• CRC code of code rate 8/9

• Turbo code

• code rate 5/6

• block length 900 bits

• decoding MAP algorithm

• iterative decoding stage 6

• Overall code rate

0.74
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Simulation Results

• 3 plotted curves

conventional
conventional decoding with hard-decision
proposed
ideal
proposed proposed decoding with error- detected
reliability
In moderate to high range slight difference
between ideal and proposed
ideal decoding with soft-decision
26
Summary of Part 1

• Soft reliability values are obtained from the
• hard-detected signals with an aid of the
• error detection.

• Turbo decoding is combined with the
  error-detected
• reliability.

• Proposed scheme approaches BER performance
• of turbo decoding in moderate to high
• signal-to-noise ratio.

27
Summary of Part 1

• Soft reliability values are obtained from the
• hard-detected signals with an aid of the
• error detection.

• Turbo decoding is combined with the
  error-detected
• reliability.

• Proposed scheme approaches BER performance
• of turbo decoding in moderate to high
• signal-to-noise ratio.

The loss due to code rate of the extra combined
error detector is unavoidable.
28
Part 1
Turbo Decoding for Hard-Detected Signals, i.e.
Optical Fiber Communication Systems (Chap.3)
Part 2
Decoding of LDPC Codes for Hard-Detected Signals,
i.e. Optical Fiber Communication Systems (Chap.4)
29
Background

• In proposed turbo decoding scheme, extra
• concatenated error detector has to be used.

• The loss due to the extra code rate (extra
• redundancy) is unavoidable.

• Extra code rate loss prevents further
  improvement
• of such proposed decoding scheme.

• In contrast, the construction of the low-density
• parity-check codes provides a scheme with
  error
• detection without extra loss of the code rate.

30
Low-Density Parity-Check (LDPC) Codes
R. G. Gallager, Low-density parity-check codes,
MIT Press

• A class of block codes with powerful decoding
• scheme (like Turbo decoding)

- A linear block code with relation
x HT 0
x
Codeword sequence
H
Parity-check matrix

• Since LDPC code is based on the parity-check
  codes,
• decoding is based on the error detection

31
Motivation of Research
Converting hard-detected signals into soft values
with an aid of the error detection Without extra
concatenated error detector
Proposed System Model
hard
soft
LDPC encoder
Reliability decision
LDPC decoder
OFC channel
Reliability decision is based on the error
detection process inside the LDPC codes.
32
Code Structure of LDPC Codes (1)
- Defined by a very sparse parity-check matrix H
parity checks
x
codeword
Number of ones row 4 column 2
x2
x1
x3
x5
x4
x7
x6
x8
x10
x9
codeword nodes
parity-check nodes
C1
C2
C3
C4
C5
33
Code Structure of LDPC Codes (2)
- Component parity-check codes i.e. C1 C5
codeword nodes
x2
x1
x3
x5
x4
x7
x6
x8
x10
x9
C1
C2
C3
C4
C5
parity-check nodes
- Interleaving effect
x3
x2
x4
x6
x5
x8
x7
x9
x1
x10
C1
C2
C3
C1
C3
C1
C1
C4
C2
C2
C5
C3
C4
C4
C5
C2
C4
C5
C5
C3
34
Reliability Decision based on Error Detection
in error
x3
x2
x4
x6
x5
x8
x7
x9
x1
x10
gg
gb
gb
bg
gg
gg
gb
state
bb
gb
bg
r3
r2
r1
r2
r2
r3
r2
r2
r3
r2
reliability

• g good state w/o detected errors

• b bad state with detected errors

35
Simulation Results

• code rate
• 2/3 and 3/4

• block length
• 900 bits

Comparing to

• uncoded case

• Reed-Solomon
• code

i.e. TAT14 Japan-USA, RS Code, 5.3 dB gain, for
7350km.
11.5dB
4.5dB
36
Summary of Part 2

• Proposed scheme shows significant performance
• of LDPC decoding for systems with
  hard-detected
• signals, i.e. OFC systems.

• It is possible to realize soft-decision decoding
• for LDPC codes with error detection based
• reliability without extra loss of code rate.

37
Conclusions
Soft reliability values are obtained with an
aid of the error detection.
Soft-decision decoding schemes are proposed on
the systems with hard-detected signals as input
of the decoder.
It is possible to realize the turbo decoding for
the high-speed optical fiber communication systems
with hard-detected signals.
38
Conclusions
It is possible to realize the LDPC decoding for
the high-speed optical fiber communication systems
with hard-detected signals without extra
concatenation of the error detectors.
Turbo codes can be applied on short
block transmission systems by using the
spread- spectrum techniques to obtain the
large interleaving size.
39
Conclusions
The proposed powerful soft-decision
decoding schemes using error-detected reliability
can be used to more applications, where
hard-detected signals are the only usable channel
outputs.
For example regenerative repeaters
40
Additional Slides
41
Simulation Results by Concatenation of RS Codes
and Turbo Codes
RS Code (255,239)
i.e. TAT14 Japan-USA, RS Code, 5.3 dB gain, for
7350km.
3dB
42
SNR Approximation for OFC Systems
on signal S1, deviation V1
Probability density functions
off signal S0, deviation V0
Error probability
1
8
Pe
exp(-x2/2)dx
2p
Q
s1-s0
Q
where
obser- vation
S0
S1
D
v1-v0
called Q-factor
For
Q5.99781
Pe
10-9
10log10
Q215.56dB
Corresponding to
43
Simulation Results of Chip-by-Chip Turbo Coding
Scheme for DS/SS Systems
AWGN
QPSK
K200 bits
Code rate 1/2
SOVA Decoding
3dB
6 Iterations