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**Capacity-approaching channel coding in use**

Ba-Zhong Shen Communication and Information theory workshop (CITW2013) ,Oct , 2013, Xi’an China

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**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

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**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

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**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

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**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

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**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

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**Yesterday: Dominance of classical Channel coding**

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**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)

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**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.

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**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

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**TCM with A punctured convolutional encoder**

DOCSIS 3.0 ITU J.83

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**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

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**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

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**Today: Capacity-approaching channel coding**

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**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

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**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

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**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

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**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

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**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

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**Satellite set-top box Turbo codes in use**

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**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

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**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

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

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**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

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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

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**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

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**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

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**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

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**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

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**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

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**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.

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**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.

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**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.

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

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**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).

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**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

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**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

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**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.

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**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

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**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

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**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.

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

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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

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**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

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**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

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**128 DSQ Mapping (labeling)**

Broadcom: IEEE P802.3an 10GBASE-T Task Force

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**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

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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.

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

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**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

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**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)

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**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

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**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

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**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.

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**Home network: MoCA 2.0 LDPC codes in use**

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**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.

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**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

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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]

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**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)

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

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**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

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**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)

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