1. Capacity-approaching channel coding in use
Ba-Zhong Shen
Communication and Information theory workshop (CITW2013) ,Oct , 2013, Xi’an China

2. High data rate Modern Technology High Demands
Data hungry world
Number of Users
OFDM
High data rate
Transmission
Video Quality
Modern Technology
High Demands
Capacity
Approaching Coding
Streaming
Speed
(Up & Down)
Error correction

3. Mobile 4G Peak Data Rate 1992 1998 1999 2000 3G 2002 2004 2007 2008
2011 4G
DL:3 Gbps
UL:1.5 Gbps
LTE Advanced
DL:100 Mbps
UL:50 Mbps
LTE
DL:28/42 Mbps
UL:11 Mbps
HSPA+
DL:14.4 Mbps
UL:5.7 Mbps
HSPA
14.4 Mbps
HSDPA
Peak Data Rate
2 Mbps
WCDMA
473 kbps
EDGE
171 kbps
GPRS
9 kbps
GSM

4. Ethernet (copper) Peak Data Rate 1973 1983 1985 1990 1998 1999 2006
2013-
40 Gbps
10 Gbps
IEEE 802.3y 100BASE-T2
IEEE 802.3a 10BASE2 thinnet coax
IEEE 802.3i 10BASE-T twisted pair
1 Gbps
IEEE BASE5 think coax
Peak Data Rate
IEEE 802.3an 10GBASE-T
IEEE 802.3bq 40GBASE-T
100 Mbps
Experimental (Coax)
IEEE 802.3ab 1000BASE-T
10 Mbps
10 Mbps
10 Mbps
2.94 Mbps

5. Home network Peak Data Rate 2004 2007 2010 2010- MoCA 2.0 (Bonded)
800 Mbps
MoCA 2.0
400 Mbps
Peak Data Rate
MoCA 1.1
175 Mbps
MoCA 1.0
125 Mbps

6. Wireless LAN Peak Data Rate 1997 1999 2003 2009 2012 2010
7 Gbps
1 Gbps
IEEE g (Better Ranges)
IEEE a (OFDM)
IEEE b (DSSS)
150 Mbps
(3 X 3 450)
IEEE ad (WiGi,60 GHz)
Peak Data Rate
IEEE ac
54 Mbps
54 Mbps
IEEE
11 Mbps
IEEE n (MIMO)
2 Mbps

7. Yesterday: Dominance of classical Channel coding

8. Channel coding in previous standards
Application
Standard
Year
Channel Code
Modulation
Date Rate
Satellite broadcasting
DVB-S
1997
Concatenated code
Outer: Reed Solomon code
Inner: 64-state convolutional code
Single carrier QPSK
27.5 Mbaud
Ethernet (copper)
1000BASE-T
1999
8-state 4D trellis code
Single carrier PAM 5
125 Mbaud
Wireless LAN
IEEE a/b/g (Wi-Fi)
64-state binary convolutional code
OFDM up to 64-QAM
≤ 54 Mbps
Mobile communication
2-2.5G
GSM,GPRS,EDGE
2000
Cyclic code and convolutional code
Single carrier
GMSK, 8-PSK
Kbps
Home network
MoCA 1.1, Home-plug and VDSL
2007
Reed-Solomon code,
convolutional code, or
Outer: RS code
Inner: 16- state 4D trellis code
OFDM up to 256-QAM
175 Mbps
Cable modem
DOCSIS 3.0
2006
Inner: Trellis cod
Single carrier up to 256-QAM
320 Mbps (e.g. 8 channel bounding)

9. Two mainly used classical channel coding methods
In 1955, Elias introduced convolutional codes as an alternative to block codes. They were used in Voyager, Mars Pathfinder, Mars Exploration Rover, and the Cassini probe to Saturn.
Capacity
1bit/s/Hz
64 states
Convolutional
8 states
Reed-Solomon
Size 4608
Uncoded
QPSK
Code rate 1/2
Binary convolutional encoder used by IEEE
Reed–Solomon codes were developed in 1960 by Irving S. Reed and Gustave Solomon, who were then staff members of MIT Lincoln Laboratory. Reed–Solomon coding is very widely used in mass storage systems to correct the burst errors associated with media defects.
8-bit RS (40,32), (44,32), (74,64), (140,128), and (208,192) codes were used for MoCA 1.

10. Trellis-coded modulation (TCM)
In his 1982 landmark paper, Gottfried Ungerboeck wrote:
“The general finding of this paper is that compared with uncoded modulation, the same amount of information can be transmitted within the same bandwidth with coding gains of 3–4 dB by simple hand-designed codes with four to eight states.”
Set-partitioning
“Channel Coding with Multilevel/Phase Signal,” IEEE IT-28, No.1, Jan. 1982

11. TCM with A punctured convolutional encoder
DOCSIS 3.0 ITU J.83

12. Concatenated coding DVB-S, DOCSIS 3.0, VDSL and etc. used concatenated
In his titled Concatenated Codes thesis, D. Forney showed “concatenation of an arbitrarily large number of codes can yield a probability of error that decreases exponentially with the over-all block length, while the decoding complexity increases only algebraically”
DOCSIS 3.0
Outer encoder
Interleave
inner encoder
DVB-S, DOCSIS 3.0, VDSL and etc. used concatenated
coding with RS outer code and trellis inner code

13. Convolutional Encoder Linear Combination and
Multidimensional TCM
In his IEEE-IT award paper, Lee-Fang Wei wrote:
“The principal conclusion is that for the same (modest) complexity (i.e., complexity less than or equal to that of the 32 state 2D code) trellis-coded modulation with multidimensional rectangular constellation is superior to using 2D constellations.”
L.-F. Wei, "Trellis-Coded Modulation Using Multidimensional Constellations,“ IEEE Trans Info. Theory, vol. IT-33, July 1987.
Convolutional Encoder
Linear Combination and
4D Set- Partitioning
2D-Constellation
Modulation
4D, 8D, or higher dimensional lattice partition.
Transmit fractional information bits per carrier.
VDSL 2
1000BASE-T

14. Today: Capacity-approaching channel coding

15. Turbo codes Iterative Decoding Encoding
In 1993 ICC’93 Geneva, C.Berrou, A.Glavieux, and P. Thitimajshim told the world: they invented “a new class of convolutional codes called Turbo codes, whose performances in terms of Bit Error Rate (BER) are close to the SHANNON limit.”
Iterative Decoding
Encoding

16. Trellis-Coded Modulation
Turbo codes vs. TCM
Uncoded
Trellis-Coded Modulation
Turbo Code
Constellation
QPSK
8-PSK
Rate 1
2/3
Info bits/s 2
# of states 4 8
512
Interleave size
2564
10240
BER = 1e-6
13.5
10.5
9.56
7.52
7.18
6.48

17. Low-density parity-check code
In 1995, D. MacKay and R.M. Neal rediscovered the largely forgotten low-density parity check code. They wrote: It can be proved that these codes are “very good,” in that sequences of codes exist which, when optimally decoded, achieve information rates up to the Shannon limit. Cryptography and Coding 5th IMA Conf. 1995
In 1997, M. Luby, M. Mitzenmacher, A. Shokrollahi, D. Spielman, and V. Steman introduced irregular LDPC codes
In 1962, R.G. Gallager published the paper entitled “Low-density Parity–Check codes” in IRE-IT. He also proposed “a simple but non-optimum decoding scheme operating directly from the channel a posteriori probabilities” and “the probability of error using this decoder on a binary symmetric channel is shown to decrease at least exponentially with a root of the block length.”
Richardson, Shokrollahi, and Urbanke, IEEE –IT Vol. 42. No

18. LDPC code vs. RS and TCM concatenated codes
256-QAM
Concatenated Code
LDPC Code
16-State Punctured Trellis Code
7-bit RS Code
30-Iteration
Decoding
Rate
19/20
122/128
8/9
Interleave
88 RS codes
Total info. size
75152 bits
16200
Overall rate
0.905
0.89
Bits/symbol
7.24
7.11
Distance to Shannon limit
BER = 1e-6
3.4 dB
1.04 dB
Standard
DOCSIS 3.0

19. LDPC code vs. concatenated code with 4-D trellis code
Rate 5/6 (0.83) G.Hn
LDPC (5184,4320)
Concatenated Rate 0.82
RS + 16-state 4D Wei TCM
64-QAM
SNR (dB)
Concatenated Code
LDPC Code
16-States 4-D Trellis Code
8-bit RS Code
Interleave
4 RS codes
Total info. size
4320 bits
Rate
11/12
135/151
5/6
Overall rate
0.8195
0.8333
Bits/symbol
4.9 5
Standard
VDSL 2
ITU G.hn

20. Satellite set-top box Turbo codes in use

21. Turbo codes for satellite set-top boxes
AMSTERDAM – September 14, 2001
Broadcom Corporation will demonstrate its 8-PSK Turbo Coding System, which increases throughput for advanced satellite broadcast services up to 50% over a commercial satellite link during the International Broadcasting Convention show in Amsterdam, September 14–18, 2001.
Top(T)
Bottom(B )
Ma ppe r
Closure trellis within interleave block
0,…, 0 uN-M-1,1,…,u1,1,u0,1
0,…, 0 uN-M-1,0,…,u1,0,u0,0
t1,1,…tM,1, uN-M-1,1,…,u1,1,u0,1
t1,0,…,tM,0, uN-M-1,0,…,u1,0,u0,
vN-1,1,…,v1,1,v0,1
vN-1,0,…,v1,0,v0,0
Closure symbols generator
Interleave
Encoder →
De-
mapping
Turbo
decoder
A Reed-Solomon code is used as an outer code with an interleaver to mitigate the error floor and burst error

22. Achievement Rate ½ Codes QPSK Irvine, California – Dec. 1, 2003
Broadcom Corporation today announced that EchoStar Communications Corp. is using Broadcom’s 8-PSK Turbo code technology across EchoStar’s newest line of DISH Network™ satellite TV receivers,…
Broadcom’s 8-PSK Turbo code is an advanced modulation and coding technology that increases information throughput by 35 percent in a given bandwidth or radio frequency link with no additional power requirements. …
8-State
Trellis Code
64-State
Trellis Code
Uncoded
1024-State
Trellis Code
8-StateTurbo Code
Interleave Size 2564,
4 Iterations
8-State Turbo Code
interleave Size 10240
8 Iterations
Shannon Limit:
1 bit/second/Hz

23. mobile communications（3G, 4G, LTE） Turbo codes in use

24. Turbo coding in 3G mobile
3G is the third-generation of mobile phone technology standards. The typical services associated with 3G include wireless voice telephony and broadband wireless data, all in a mobile environment.
Turbo codes were introduced into CDMA2000 1X, the first 3G (IMT-2000) technology deployed.
October 2000.
Interleaver
Sizes: 250,506,1018,2042,4090
Function:
Generate the interleaving positions through a counter
Modify generated addresses through
LUT
Reverses the order of the bits.
Output of encoder: x,y0,y1,x’,y’0,y’1, …
Puncturing for code rate
x and x’ can not be all punctured
1/6 turbo encoder
3GPP2 C.S0024

25. Turbo coding in 3GPP
Universal Mobile Telecommunication System (UMTS)/WCDMA
3GPP TS , Release 6, 2005
Both Turbo encoder and interleaver are modified from CDMA2000.
Output of the encoder: x1, z1, z'1, x2, z2, z'2, …
xk never be punctured.
Interleaver sizes: 40 to 5144.
Matrix based interleaver
The free distance of WCDMA Turbo code is 21.
The free distance of CDMA2000 Turbo code is 19.
Claim: 0.5 dB gain.
S-H. Ryu, KAIST, Information and Communication University, Korea, 2001

26. Decision Channel coding for LTE Channel Coding Proposed schemes:
Long Term Evolution (LTE) is an evolution of the GSM/UMTS standards. The goal of LTE is to increase the capacity and speed of wireless data networks using new digital signal processing techniques and modulations.
LTE is the redesign and simplification of the network architecture to an IP-based system with significantly reduced transfer latency compared to the 3G architecture.
Channel Coding
Proposed schemes:
Turbo code
LDPC code
Criteria:
BLER ~1e-4 with HARQ
Simulation Results:
No significant difference
Decision
RAN1 Mr. Chairman, Dirk Gerstenberger of Ericsson, proposed the conclusion and explained his opinion, … The problem is not TC but interleaver structure; therefore, we stick Rel-6 TC using contention free interleaver … Mr. Chairman clarified that we should minimize the standard option from the viewpoint of the standard classic for making the implementation issue much less.
3GPP TSG RAN WG1 #46 Tallinn, Estonia, August, 2006

27. LTE Turbo code Interleavers
In this paper, a class of deterministic interleavers for Turbo codes (TCs) based on permutation polynomials over ZN is introduced. The main characteristic of this class of interleavers is that they can be algebraically designed to fit a given component code.
J. Sun and O. Y. Takeshita, “Interleavers for Turbo codes using permutation polynomials over integer rings,” IEEE Trans. Inform. Theory, vol. 51, no. 1, pp. 101—119, Jan
Motorola, R , 3GPP TSG-RAN WG1 #47bis, Jan. 2007 ,
QPP: Quadratic Polynomial Permutation
where K is the information size.
LTE interleaver: QPP
Szes: 40 ~ 6144
Total number of interleavers: 188

28. Parallel Decoding WCDMA (UMTS) 3G HSPA HSDPA/ HSUPA HSPA+ LTE (CAT 3)
Maximum downlink speed
384 kbps
14 Mbps
28 Mbps
100 Mbps
300 Mbps
Maximum uplink speed
128 kbps
5.7 Mbps
11 Mbps
50 Mbps
75 Mbps
CAT 1
CAT 2
CAT 3
CAT 4
CAT5
DL peak rate (Mbps) 5 50
100
150
300
Number of code blocks per transport block 1 9 13 25
Turbo clock rate (MHz)
　　# Parallel processors required 7 15 23 60
200 4 11 3 14
400 2
500 8

29. Contention-free memory mapping
Parallel decoding needs contention-free memory mapping.
Memory Banks
Contention-Free
Source: Tarable et al. paper
time 1
time 2
time 2
For any code and any choice of the scheduling of the
reading/writing operations, there is a suitable mapping of the variables in the memory that grants a collision-free access
A. Tarable, S. Benedetto and G. Montorsi “Mapping Interleaving Laws to Parallel Turbo and LDPC Decoder Architectures,” IEEE Trans. on Information Theory, Vol. 50, No. 9, pp , Sept. 2004

30. Fighting for surviving
Release 6 interleavers: ad-hoc contention-free mapping (Samsung, Nortel and Panasonic)
R GPP TSG RAN WG1 Meeting#47 Riga, Latvia, Nov , 2006
QPP: ad-hoc contention-free mapping (Ericsson)
R GPP TSG RAN WG1 Meeting#47bis, Sorrento, Italy, Jan 15th-19th, 2007

31. Systematic Contention-free mappings for QPP
Bit Index
(before or after interleaving)
Bank index
A. Nimbalker, T. E. Fuja, D. J. Costello, Jr. T. K. Blankenship, and B. Classon, “Contention-Free Interleavers,” IEEE ISIT 2004, Chicago, USA, June 27–July 2, 2004.
Restriction: The number of parallel processors must be a divisor of the interleave size.
Previously existed
Bit Index
(before or after interleaving)
Bank index
C|N with C > P and window size W ≥ N/P and gcd(W, C) = 1.
Broadcom: R , 3GPP TSG RAN WG1 #47bis, Sorrento, Italy, Jan 15th-19th, 2007
T.K. Lee and B-Z. Shen “A Flexible Memory-Mapping Scheme for Parallel Turbo Decoders with Periodic Interleavers,” IEEE ISIT2007, Nice, France, June 24–June 29, 2007.
No restriction: Allows any possible number of parallel processors.
Newly developed
Example: Consider CAT 5 (DL data rate = 300 Mbps) with Turbo decoding clock rate = 100 MHz→60 parallel processors.
Interleave size N = 6144(#188 LTE interleaver) = 3*211.
“Div” method needs at least 96 parallel processors.
‘Mod” method provides exactly 60 parallel processors.

32. Circular-Buffer Rate Matching (puncturing and shortening)
Turbo Encoder S P1 P2
Subblock
Interleaver I
Interleaver II
Interleaved
Interleaved and interlaced
P1 and P2
Circular buffer
3rd TX
2nd TX
1st TX
One code block
Starting
position
Easy to implement.
Praised by most engineers.
Independent of the mother code.
L. Korowajczuk, Designing CDMA2000 Systems, John Wiley and Sons, 2004.

33. Rate matching optimization
Broadcom “Rate matching proposal based on 15 period 8 optimal puncturing patterns,” R , 3GPP TSG RAN WG1 #49, Kobe, Japan, May 7th–11th, 2007.

34. Digital video Broadcast（DVB） Satellite set-top box and others LDPC codes in use

35. LDPC code for DVB-S2, DVB-T2, and DVB-C2
QPSK
w/o BCH
w/BCH
(In 2003) After closely examining several candidates in terms of performance and estimated ASIC size, the (DVB-S2) committee chose a solution based on Low-Density Parity-Check (LDPC) codes, which actually delivered more than 35% throughput increase with respect to DVB-S.
(Hughes Network System) M. Eroz, F.-W. Sun, and L.-N. Lee, “DVB-S2 low density parity check codes with near Shannon limit performance,” International Journal on Satellite Communication Networks, vol. 22, no. 3, May–June 2004
DVB-S2 FEC system shall perform:
Outer coding (BCH).
Mitigates error floor (12 bits errors).
Inner Coding (LDPC).
Bit interleaving.
BICM (Bit-Interleaved Coded Modulation).

36. DVB-S2 LDPC code design I: RA code
Accumulator
RA (Repeat-Accumulate) Code
D. Divsalar, H. Jin, and R. J. McEliece. "Coding theorems for ‘turbo-like’ codes." 36th Allerton Conf. on Communication, Control and Computing, Sept., 1998
Irregular Repeat–Accumulate Codes
H. Jin, A. Khandekar, and R. McEliece, Proceedings of the 2nd symposium - 2000 in Brest, France
Tanner graph of RA code

37. DVB-S2 LDPC codes ARE IRA codes
k information bits b0, b1, …, bk
Repetition: Every bi repeat ri times, i = 0, ..., k-1 (bit degree distribution).
Permutation: Interleave m = r0 + r1 +…+ rk-1 bits to generate y0, y1, …, ym-1.
Accumulation: Generate parity bits (connect check equations).
Final accumulation: p0, p1 = p0+p1,…, pv = pv-1+pv, …, pn-k-1 = pn-k-2+pn-k-1 (parity bits)
IRA code
DVB-S2 codes
DVB-S2 codes are IRA codes.
Permutation in general: 1. Uses a look-up table (LUT) to select a check-node x for a certain bit node.
2. The next 359 consecutive bit nodes are mapped to the 359 check nodes cyclic shifted from x.
Example: Rate 2/3 (64800,43200) code.
Repetition: 12*360 bits repeat 13 (degree 13) times and another 108*360 bits repeat 3 time (degree 3)
→ m = 480*360.
Permutation: LUT of 12 sets of 13 random integers and 108 sets of 3 random integers.
Accumulation: Take a = 8 → m/a = 21600

38. DVB-S2 LDPC code design II: hardware friendly
Decoder-First Code Design
The natural approach for the design of an error correction system is first to construct a code, then define the hardware structure of the decoder. … This paper proposes to operate the other way: in the first step, an efficient hardware structure is chosen and, in the second step, a code is constructed that adequately fits this structure.
E. Boutillon, J. Castura, and F. R. Kschischang, in Proceedings of the 2nd International Symposium on Turbo Codes and Related Topics, Brest, France, Sept
In the Recent Results session of the 2000 International Symposium on Information Theory, R.M. Tanner presented a (155,64) LDPC code with a minimum distance of 20; the code's parity check matrix was constructed from shifted identity matrices (i.e., permutation matrices) …
Tanner’s approach was later generalized to the codes with varying block lengths and rates.
D. Sridhara,T. Fuja and R.M. Tanner, “Low density parity check codes from permutation matrices,” Conf. On Info. Sciences and Sys., The John Hopkins University, March 2001.
The expanded matrix contains L permuted identity matrices, each one denoted as Tu,v .
VNU: Variable-node computation unit.
CNU: Check-node computation unit
Quasi-cyclic LDPC
(QC-LDPC) code
H. Zhong and T. Zhang, T. “Design of VLSI Implementation-Oriented LDPC Codes,” The 58th IEEE Vehicular Technology Conference, VTC 2003.

39. DVB-S2 codes are QC-LDPC
Example: An IRA code with DVB-S2 permutation.
Rate ½ (1248, 624) code.
Its parity-check matrix corresponds to a matrix constructed by cyclic-shifted identity matrices.
Cyclic-shifted identity matrix size: 52
Integers m: an m position right shifted 52 x 52 identity matrix
Empty cell: a 52 x 52 all-zero matrix
Two cyclic-shifted identity matrices on top of each other D

40. DVB-S2 codes achievement
DVB-S2 satellite receiver
12 size 64K and 12 size 16K LDPC codes
With a 12 bits of error correction BCH outer code to mitigate error floor.
32% ~ 36% throughput increase.
Eroz, Sun, and Lee, “DVB-S2 low density parity check codes with near Shannon limit performance,” 2004

41. Is DVB-S2 LDPC code really better than turbo code?
DVB-S2 code
Turbo code
Rate
1/2
# Information bits
32400
10240
(interleave size)
# iterations 40 8
Both LDPC decoder and Turbo decoder
can be operated in parallel.

42. 10GBase-T Ethernet(IEEE 802.3an) LDPC codes in use

43. 10G Ethernet
10GBASE-T/IEEE 802.3an
A standard released in 2006 to provide 10 Gb/s connections over unshielded or shielded twisted-pair cables, over distances of up to 100 meters.
The main objective of 10GBASE-T is to provide a cost-effective and highly scalable 10 Gigabit Ethernet implementation over structured copper cabling infrastructure that is widely used in data centers
Cisco
Robert M. Metcalfe (1973)
10GBASE-T, the fastest growing 10GE connectivity solution in data centers, is expected to exceed all other 10GE alternatives by 2015 and reach more than 30 million ports in 2016
Crehan Research
wikipedia

44. Constellation selection for 10GBase-T
KeyEye Proposed
(Campopiano and Glazer 1962)
Teranetics Proposed
128-Point “Doughnut” Constellation
(Square)
Broadcom Proposed
(Wei 1994)
128-Point Double Square Constellation
(Square)
Tomlinson-Harashima precoder (THP) is used for severe amplitude distortion in the frequency domain with a known channel impulse response.
Average Transmitted Signal Power (Without THP)
Minimum Squared Euclidean Distance
Average Transmitted Signal Power (with THP) (2/3)L2 (*)
Cross 82 4
96 (L=12)
Doughnut
106
Double square 85 8
(L=16)
128-DSQ provides more coding gain than the other two:
* L.-F. Wei, “Generalized Square and Hexagonal Constellations for Intersymbol-Interference Channels with Generalized Tomlinson-Harashima Precoders, “IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 42, NO. 9, SEPTEMBER 1994

45. Set-partitioning using capacity approaching code
M bits/symbol constellation
L level set-partition → L coded bits and M – L uncoded bits
P(e)ISS-L: Probability of intra-subset (ISS) of error (error rate of uncoded bits)
(AWGN channel)
S3,0
S3,1
S3,2
S3,3
S3,4
S3,5
S3,6
S3,7
ΔL: Minimum intra-distance of SL,I, usually
SL,i: A subset in level L (L-coded bits)
Δ0: Minimum distance of the starting lattice
Code 4 bits per symbol.
10*log10(2L) = 3*L dB set-partitioning.
Broadcom: IEEE P802.3an 10GBASE-T Task Force

46. 128 DSQ Mapping (labeling)
Broadcom: IEEE P802.3an 10GBASE-T Task Force

47. RS Code-Based Regular LDPC Code
LDPC code selection
RS Code-Based Regular LDPC Code
A simple RS-based algebraic method for constructing regular LDPC codes with a girth of at least 6 has been presented. Construction gives a large class of regular LDPC codes in Gallager’s original form that perform well with the SPA.
I. Djurdjevic, J. Xu, K. Abdel-Ghaffar, and S. Lin,
IEEE COMMUNICATIONS LETTERS, VOL. 7, NO. 7, JULY 2003
Dimension 2 Reed-Solomon code C over GF(2s)
GF*(2s)={αi |i=-∞,0,1,…,2s-2} , α-∞=0,
Codeword size: ρ (≤2s-1)
Minimum distance: ρ-1
Location mapping:
αi →Z(αi) = (0,…,0,1,0,…,0), a size 2s vector, 1 at location i
Regular LDPC matrix
γ coset codes
Tanner graph girth ≥ 6.
Bit node degree = . Check node degree = .
LDPC code dmin

48. LDPC code selection
KeyEye
T. Richardson
“Error Floors of LDPC Codes”
LDPC (1024,833)
Broadcom
IEEE P802.3an 10GBASE-T Task Force
Djurdjevic et. RS-based (2048,1732) LDPC code: dmin= 8
Broadcom GRS -based (2048,1732): dmin=14
Final decision: GRS-based (2048,1723) code
Improved G and H matrices are defined in IEEE 802.3an spec..
Minimum distance calculations were provided by Marc Fossorier.

49. Wireless LAN: Wi-Fi (IEEE 802.11) LDPC codes in use

50. LDPC Code structure for IEEE 802.11n
The main objective of an IEEE n system is to achieve a maximum PHY data rate around 500 Mbps with four transmit antennas and a channel width of 40 MHz.
Major advanced technology:
MIMO-OFDM
Optional advanced techniques for increasing range and reliable communications:
Adaptive beamforming
Space-time block coding (STBC)
Low-Density Parity-Check (LDPC) coding
Parity-Check matrices: CSI-SM based
H = [H1 H0]
H0 corresponds to parity bits.
WWiSE
World Wide Spectrum
Efficiency consortium H0
TGn Sync H0
1/2
1/2 1
2/3 D
2/3
3/4
3/4 D 1
5/6
5/6 D 1 D 1

51. TGn Sync: using Richardson and Urbanke encoding
Efficient Encoding of Low-Density Parity-Check Codes, IEEE TRANSACTIONS ON INFORMATION THEORY, VOL. 47, NO. 2, FEBRUARY 2001
Richardson-Urbanke Encoding k
n-k-g g
LDPC matrix
Information data:
is a nonsingular matrix.
When
1st part of check bits:
2nd part of check bits: 1
TGn SYNC H0=
(1-0-1)

52. WWiSE: IRA code structure used in DVB-S2
WWiSE Structure: IRA Code
(Used in DVB-S2) D
Column and row permuting
H0=
Hughes Network Systems, STMicroelectronics, Texas Instruments and Trellisware: IEEE TGn
AWGN
Better performance
Redundancy-bit nodes
Information-bit nodes
Check
nodes …
Large open loop
Tanner Graph

53. Final structure Code constraints given by JP LDPC ad hoc group
H0 uses “1-0-1” structure for RU encoding.
24 submatrices columns, submatrices size: 81,54, and 27 and maximal number of nonzero submatrices is 88.
12 LDPC codes (4 rates, 3 sizes) provided by Broadcom, Conexant, Hughes Network, Intel, Marvell, Motorola, Nokia, Nortel, STMicroelectronics, Texas Instruments, and Trellisware.
AWGN
B TGn Channel
W. A. Syafei, R. Yohena, H. Shimajiri, T. Yoshida, M. Kurosaki, Y. Nagao, B. Sai, and H. Ochi, Performance Evaluation and ASIC Design of LDPC Decoder , IEEE n CCNC th IEEE Jan. 2009

54. Usage LDPC codes were never used in IEEE 802.11n production.
802.11ac, the emerging standard from the IEEE, is like the movie The Godfather Part II. It takes something great and makes it even better ac is a faster and more scalable version of n ac couples the freedom of wireless with the capabilities of Gigabit Ethernet CISCO
IEEE ac achieves its raw speed increase by doing the following three things:
Increasing the channel bonding bandwidths:
Up to 80 MHz or even 160 MHz in IEEE ac versus 40 MHz in IEEE n.
Increasing the modulation density:
Up to 256-QAM in IEEE ac versus 64-QAM in IEEE n.
Increasing the Multiple Input Multiple Output (MIMO) spatial streams.
Up to eight in IEEE ac versus four in IEEE n.
LDPC codes become relevant and are in IEEE ac products.

55. Home network: MoCA 2.0 LDPC codes in use

56. MoCA: a home networking
The Multimedia over Coax Alliance (MoCA®) is the universal standard for home entertainment networking. MoCA is the only home entertainment networking standard in use by all three pay TV segments: cable, satellite, and IPTV. Networks that support the current MoCA specification can provide multiple streams of HD video, deliver up to 175 Mbps net throughput, and offer an unparalleled user experience via parameterized quality of service (PQoS).
MoCA is used in high SNR environment.
Target maximal throughput at high SNR with large constellations.
Broadcom: MoCA 2.0 F2F meeting
Considered LDPC code size: 4K
Considered Code rates:
90% code for high throughput
75% code for good robustness
85% code in between
To achieve a high data rate, we picked a 90% code.

57. Narrowband (NB) interferers will slightly reduce the maximum PHY rate
Narrowband ingress noise with three Interferers
Sub-carrier number dB
90% code
32 QAM
AWGN
80% code
64 QAM
64 QAM (4.8b/s)
NBI = 25 dBc
32 QAM(4.5b/s)
NBI = 28 dBc
3 dBc difference
Broadcom 90% code structure
Irregular
Degree 6 bits in information
Degree 2 bits in parity parts x H0 x
Entropic 80% code structure
Regular
Degree 6 bits H0

58. dBc (decibels relative to the carrier) is the power ratio of a signal to a carrier signal, expressed in decibels. For example, phase noise is expressed in dBc/Hz at a given frequency offset from the carrier. dBc can also be used as a measurement of SFDR between the desired signal and unwanted spurious outputs resulting from the use of signal converters such as a digital-to-analog converter or a frequency mixer.
If the dBc figure is positive, then the relative signal strength is greater than the carrier signal strength. If the dBc figure is negative, then the relative signal strength is less than carrier signal strength.
Although the decibel (dB) is permitted for use alongside SI units, the dBc is not.[1]

59. Mitigate narrowband ingress noise (Continued)x
85% code structure
Regular in information
Low-triangular in parity
MoCA 2.0 adopted the Broadcom 85% 4K LDPC code.
Compare to RS Code (1024-QAM AWGN)
An 85% code provides 0.5 dB spectral efficiency gain over an 80% code.
2.42dB
1.914dB
An 85% code is short by 1 dB compared to an ENTR 80% code.
(Narrow band ingress noise)

60. Wireless LAN: WiGig (IEEE 802.11) LDPC codes in use

61. Wigig: IEEE 802.11ad Challenge to LDPC: Very high data rate 7 Gbps
The WiGig standard, also known as the IEEE ad standard, is similar to the existing Wi-Fi standards but uses the 60 GHz frequency band, instead of the 5 GHz and 2.4 GHz bands. For this reason WiGig is capable of offering wireless speeds up to 7 Gbps, or some five times the speed of the latest Wi-Fi standard, the IEEE ac.
The main drawback of WiGig is the range, which is much shorter than that of Wi-Fi. Still, the high data rates mean that it can be used in data-intensive applications, or to connect adjacent devices, such as a tablet sitting next to a big-screen TV CNET
The WiGig/IEEE ad PHY layer uses a single carrier (SC) and OFDM to simultaneously enable low-power and high-performance applications.
Challenge to LDPC:
Very high data rate 7 Gbps
Low-power decoder
Use 672-bit block length corresponding to OFDM symbol size.
336 subcarriers with QPSK modulation  672 bits
Different modulation: QPSK, 16-QAM, and 64-QAM
Different code rates: 1/2, 5/8, 3/4, and 13/16

62. Constant block-length multiple rate codes [reused LDPC code set]
A. I. Vila Casado, W.-Y. Weng, S. Valle, and R. D. Wesel, “Multiple Rate Low-Density Parity-Check Codes with Constant Blocklength,”, IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 57, NO. 1, JANUARY 2009 1 2 3 4 5 6 3
2+5 6
1+4
1+4
2+5
3+6
1+3+5
2+4+6
merge
merge
merge

63. High throughput decoding
Layer decoding for QC-LDPC code (CSI-SM-based parity-check matrix)
Major difference to standard BP decoding: updating bit information in every layer.
One layer = L row sub-matrices
First proposed by M. Mansour and N. Shanbhag in “Turbo decoder architectures for low-density parity-check codes.” Global Telecommunications Conference, GLOBECOM '02. IEEE, Nov
Memory saving improvement given by D.E. Hocevar in "A reduced complexity decoder architecture via layered decoding of LDPC codes," IEEE SiPS 2004 pp , Oct
The number of iterations is reduced to almost half.
Source: P. Radosavljevic, LDPC Decoding Algorithms & Implementation ,Rice University
Three layers
Parity-check matrix of C
Layer decoding
Source: M. Mansour and N. Shanbhag, Turbo decoder architectures for low-density parity-check codes

64. Combining layer decoding and a reused code set
Column weight 1 per layer
Row 1+row 2
Column weight 1 per layer
Row 3+row 4
IEEE c high-rate wireless personal area networks (WPANs)
The first proposal suggests using IEEE c LDPC code set.

65. It is Channel dependent
AWGN Channel
Fading Channel (Suitable for IEEE ad)
c LDPC
c LDPC
A call for introducing a new code set was made.
(Key: high throughput and low-power decoding)

66. In-place code construction
Higher rate codes are constructed from lower rate codes by:
Removing rows from the top of the parity-check matrix
Adding non-null CSI submatrices to the lower rows to maintain the column weight.
Ensuring that column weight 1 per layer property is preserved.
Minimizing changes to existing non-null CSI submatrices. 40 - 38 13 5 18 34 35 27 30 2 1 36 31 7 10 41 12 20 15 6 39 28 3 29 22 4 23 21 14 24
Rate 1/2
Rate 5/8 20 36 34 31 7 41 - 10 30 27 18 12 14 2 25 15 6 35 40 39 28 3 29 22 4 24 23 21 9 13
Row 1 5
Rate ½ Base Code
Remove the first 2 rows 7 6 5 4 3 2 1 40 - 38 13 5 18 34 35 27 30 2 1 36 31 7 10 41 12 20 15 6 39 28 3 29 22 4 23 21 14 24
Remove the first 2 rows 35 19 41 22 40 39 6 28 18 17 3 - 29 30 8 33 4 27 20 24 23 37 31 11 21 32 9 12 13 25 34 14 15
Layer 1: 0+2, Layer 2: 1+3, Layer 3: 4+6, Layer 4: 5+7
In-place code set was adopted by IEEE ad
Rate 3/4
Remove the first 1 rows
Rate 13/16

67. Fully parallel v. layer In a 224 ns decode time:
1% Target BLER
In a 224 ns decode time:
A fully parallel decoder can complete 22 iterations.
A layer decoder can complete 5 iterations.
A fully parallel decoder has a 0.7 dB advantage.
A. Blanksby, B.-Z. Shen, and J. Trachewsky, “LDPC code set for mmWave communication,” Proceedings of the 2010 ACM international workshop on mmWave communications: from circuits to networks

68. Cable modem LDPC codes in use

69. DOCSIS 3.1 and EPOC
Data Over Cable Service Interface Specification (DOCSIS)
An international telecommunications standard that permits the addition of high-speed data transfer to an existing cable TV (CATV) system. The DOCSIS™ 3.1 platform will support capacities of at least 10 Gbps downstream and 1 Gbps upstream.
EPON (Ethernet Passive Optical Network) Protocol over Coax (EPoC)/
IEEE 802.3bn
The transparent extension of an IEEE Ethernet PON over a cable operator's Hybrid Fiber-Coax (HFC) network. From the service provider's perspective, the use of the coax portion of the network is transparent to the EPON protocol operation in the Optical Line Terminal (OLT), thereby creating a unified scheduling, management, and Quality of service (QoS) environment that includes both the optical and coax portions of the network.
DOCSIS Version
Downstream Rate/Channel
Upstream Rate/Channel
Maximum Number of Channels
1.x
42.88 Mbps
10.24 Mbps 1
2.0
30.72 Mbps
3.0
No limit
3.1
1.7 Gbps (unofficial)
500 Mbps (unofficial)
DOCSIS Version
Data Encoding
Largest Modulation
Channel Coding
3.0
Single
256-QAM
Concatenated coding (convolutional and RS codes)
3.1
OFDM
4096-QAM
LDPC
DOCSIS 3.1 standard activity has not been publicly disclosed.
EPoC IEEE 802.3bn task force is open to the public.

70. Coding partial bits per symbol (set-partitioning)
1024-QAM
Broadcom: IEEE 802.3bn Task force Sept., 2012
2.127 dB
1.29 dB
Six uncoded bits use 64-QAM mapping (Gray).
Four coded bits use 16-QAM mapping (Gray).
Bits/ Symbol
Number of Coded Bits
LDPC Code
Inner Code
Distance to = 1e-9
DVB-C2/S2
8.785 10
(16200,14400)
BCH (t = 12)
2.13 dB
Partially coded 9 4
(12000,9000) X
1.29 dB
Partially coded FEC is more spectrally efficient and less complex.

71. Impulse noise impact Burst impacted LDPC coded bits Partial coded FEC
Cyclic prefix
AWGN noise
Burst duration
One OFDM symbol
SNRimpulse
A burst of impulse noise may impact all subcarriers of one OFDM symbol or two consecutive OFDM symbols in one FEC frame.
A method to protect the damage caused by impulse noise:
Use time interleaving to distribute symbol errors across multiple FEC frames.
N sub-carriers apart
Burst impacted sub-carriers
Decoder may know where it is and its SNR
Non-impacted sub-carriers
After de-interleaving
Burst impacted LDPC coded bits
Decoded by LDPC soft-decision decoder
Helped by LDPC coded bits from other sub-carriers
Burst impacted uncoded bits
Recovered by decoded code bits and Euclidean distance
No help from other sub-carrier bits
One burst impacted
sub-carrier
LDPC
coded
uncoded
Need another FEC code
to protect uncoded bits
Partial coded FEC

72. LDPC code fop EPoC (16200,14400) LDPC codes on 4096-QAM
EPoC (IEEE 802.3bn) accepted Broadcom LDPC code set as downstream and upstream FEC for FDD.
LDPC codes:
8/9 (16200,14400)
28/33 (5940,5040)
3/4 (1120, 840)
No outer BCH code
Code all bits per symbol
No column-twisted bit interleaving
Broadcom: IEEE 802.3bn task force, July 2013
(16200,14400) LDPC codes on 4096-QAM
Burst Duration
 Burst SNR
DVBC2 87.8%
EPoC 89%
20 μs symbol
(two affected)
16 μs
20 dB 11
247.5 μs 10
225 μs
5 dB 21
472.5 μs 20
450 μs
40 μs symbol 9
382.5 μs 8
340 μs 19
807.5 μs 18
765 μs
Minimum depth and background SNR to achieve BER=1e-8 (4096-QAM, 30 iterations)

73. Thanks!