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1 Broadcom Proprietary and Confidential. © 2013 Broadcom Corporation. All rights reserved. CAPACITY-APPROACHING CHANNEL CODING IN USE Ba-Zhong Shen Communication.

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Presentation on theme: "1 Broadcom Proprietary and Confidential. © 2013 Broadcom Corporation. All rights reserved. CAPACITY-APPROACHING CHANNEL CODING IN USE Ba-Zhong Shen Communication."— Presentation transcript:

1 1 Broadcom Proprietary and Confidential. © 2013 Broadcom Corporation. All rights reserved. CAPACITY-APPROACHING CHANNEL CODING IN USE Ba-Zhong Shen Communication and Information theory workshop (CITW2013),Oct , 2013, Xi’an China

2 2 Broadcom Proprietary and Confidential. © 2013 Broadcom Corporation. All rights reserved. DATA HUNGRY WORLD Number of Users Video Quality Streaming Speed (Up & Down) Streaming Speed (Up & Down) OFDM Capacity Approaching Coding Capacity Approaching Coding Transmission Error correction

3 3 Broadcom Proprietary and Confidential. © 2013 Broadcom Corporation. All rights reserved. MOBILE G kbps GSM 171 kbps GPRS 473 kbps EDGE 14.4 Mbps HSDPA DL:28/42 Mbps UL:11 Mbps HSPA+ DL:100 Mbps UL:50 Mbps LTE DL:3 Gbps UL:1.5 Gbps LTE Advanced 2 Mbps WCDMA DL:14.4 Mbps UL:5.7 Mbps HSPA Peak Data Rate 4G

4 4 Broadcom Proprietary and Confidential. © 2013 Broadcom Corporation. All rights reserved. ETHERNET (COPPER) Mbps Experimental (Coax) 10 Mbps IEEE BASE5 think coax 10 Mbps 100 Mbps 10 Gbps 40 Gbps 10 Mbps 1 Gbps Peak Data Rate IEEE 802.3a 10BASE2 thinnet coaxIEEE 802.3i 10BASE-T twisted pair IEEE 802.3y 100BASE-T2 IEEE 802.3ab 1000BASE-T IEEE 802.3an 10GBASE-TIEEE 802.3bq 40GBASE-T

5 5 Broadcom Proprietary and Confidential. © 2013 Broadcom Corporation. All rights reserved. HOME NETWORK Mbps MoCA Mbps MoCA Mbps 800 Mbps Peak Data Rate MoCA 2.0 (Bonded)

6 6 Broadcom Proprietary and Confidential. © 2013 Broadcom Corporation. All rights reserved. WIRELESS LAN Mbps IEEE Mbps IEEE a (OFDM) 11 Mbps 150 Mbps (3 X 3 450) 7 Gbps 54 Mbps 1 Gbps Peak Data Rate IEEE b (DSSS) IEEE g (Better Ranges) IEEE n (MIMO) IEEE ac IEEE ad (WiGi,60 GHz)

7 7 Broadcom Proprietary and Confidential. © 2013 Broadcom Corporation. All rights reserved. YESTERDAY: DOMINANCE OF CLASSICAL CHANNEL CODING

8 8 Broadcom Proprietary and Confidential. © 2013 Broadcom Corporation. All rights reserved. CHANNEL CODING IN PREVIOUS STANDARDS

9 9 Broadcom Proprietary and Confidential. © 2013 Broadcom Corporation. All rights reserved. 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. 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. Capacity 1bit/s/Hz 64 states Convolutional 8 states Convolutional Reed-Solomon Size 4608 Uncoded QPSK Code rate 1/2

10 10 Broadcom Proprietary and Confidential. © 2013 Broadcom Corporation. All rights reserved. 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.” 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.” “Channel Coding with Multilevel/Phase Signal,” IEEE IT-28, No.1, Jan Set-partitioning

11 11 Broadcom Proprietary and Confidential. © 2013 Broadcom Corporation. All rights reserved. TCM WITH A PUNCTURED CONVOLUTIONAL ENCODER DOCSIS 3.0 ITU J.83

12 12 Broadcom Proprietary and Confidential. © 2013 Broadcom Corporation. All rights reserved. CONCATENATED CODING Outer encoder Interleave inner encoder 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” DVB-S, DOCSIS 3.0, VDSL and etc. used concatenated coding with RS outer code and trellis inner code DOCSIS 3.0

13 13 Broadcom Proprietary and Confidential. © 2013 Broadcom Corporation. All rights reserved. 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 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 Convolutional Encoder Linear Combination and 4D Set- Partitioning 2D-Constellation Modulation 1)4D, 8D, or higher dimensional lattice partition. 2)Transmit fractional information bits per carrier. VDSL BASE-T

14 14 Broadcom Proprietary and Confidential. © 2013 Broadcom Corporation. All rights reserved. TODAY: CAPACITY-APPROACHING CHANNEL CODING

15 15 Broadcom Proprietary and Confidential. © 2013 Broadcom Corporation. All rights reserved. TURBO CODES 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 16 Broadcom Proprietary and Confidential. © 2013 Broadcom Corporation. All rights reserved. TURBO CODES VS. TCM

17 17 Broadcom Proprietary and Confidential. © 2013 Broadcom Corporation. All rights reserved. LOW-DENSITY PARITY-CHECK CODE 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.” 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 Richardson, Shokrollahi, and Urbanke, IEEE –IT Vol. 42. No

18 18 Broadcom Proprietary and Confidential. © 2013 Broadcom Corporation. All rights reserved. LDPC CODE VS. RS AND TCM CONCATENATED CODES 256-QAM

19 19 Broadcom Proprietary and Confidential. © 2013 Broadcom Corporation. All rights reserved. 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)

20 20 Broadcom Proprietary and Confidential. © 2013 Broadcom Corporation. All rights reserved. SATELLITE SET-TOP BOX TURBO CODES IN USE

21 21 Broadcom Proprietary and Confidential. © 2013 Broadcom Corporation. All rights reserved. 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, 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, 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 Top(T) Bottom(B ) Ma ppe r Closure trellis within interleave block 0,…, 0 u N-M-1,1,…,u 1,1,u 0,1 0,…, 0 u N-M-1,0,…,u 1,0,u 0,0 t 1,1,…t M,1, u N-M-1,1,…,u 1,1,u 0,1 t 1,0,…,t M,0, u N-M-1,0,…,u 1,0,u 0, v N-1,1,…,v 1,1,v 0,1 v N-1,0,…,v 1,0,v 0,0 Closure symbols generator Interleave Encoder → →

22 22 Broadcom Proprietary and Confidential. © 2013 Broadcom Corporation. All rights reserved. QPSK ACHIEVEMENT 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,… 35 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. … 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,… 35 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. … Rate ½ Codes 8-State Trellis Code 64-State 8-State Turbo Code interleave Size Iterations Shannon Limit: 1 bit/second/Hz 1024-State Trellis Code Uncoded 8-StateTurbo Code Interleave Size 2564, 4 Iterations

23 23 Broadcom Proprietary and Confidential. © 2013 Broadcom Corporation. All rights reserved. MOBILE COMMUNICATIONS ( 3G, 4G, LTE ) TURBO CODES IN USE

24 24 Broadcom Proprietary and Confidential. © 2013 Broadcom Corporation. All rights reserved. TURBO CODING IN 3G MOBILE 1/6 turbo encoder 3GPP2 C.S0024 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 G 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  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,y 0,y 1,x’,y’ 0,y’ 1, …  Puncturing for code rate  x and x’ can not be all punctured

25 25 Broadcom Proprietary and Confidential. © 2013 Broadcom Corporation. All rights reserved. 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: x 1, z 1, z' 1, x 2, z 2, z' 2, …  x k never be punctured. Interleaver sizes: 40 to 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 26 Broadcom Proprietary and Confidential. © 2013 Broadcom Corporation. All rights reserved. CHANNEL CODING FOR LTE 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. 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. 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 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 Proposed schemes:  Turbo code  LDPC code Channel Coding Criteria:  BLER ~1e-4 with HARQ Simulation Results:  No significant difference

27 27 Broadcom Proprietary and Confidential. © 2013 Broadcom Corporation. All rights reserved. LTE TURBO CODE INTERLEAVERS QPP: Quadratic Polynomial Permutation where K is the information size., In this paper, a class of deterministic interleavers for Turbo codes (TCs) based on permutation polynomials over Z N 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 In this paper, a class of deterministic interleavers for Turbo codes (TCs) based on permutation polynomials over Z N 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 LTE interleaver: QPP Szes: 40 ~ 6144 Total number of interleavers: 188

28 28 Broadcom Proprietary and Confidential. © 2013 Broadcom Corporation. All rights reserved. PARALLEL DECODING CAT 1CAT 2CAT 3CAT 4CAT5 DL peak rate (Mbps) Number of code blocks per transport block Turbo clock rate (MHz) # Parallel processors required

29 29 Broadcom Proprietary and Confidential. © 2013 Broadcom Corporation. All rights reserved. Parallel decoding needs contention-free memory mapping. CONTENTION-FREE MEMORY MAPPING 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 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 Memory Banks Contention-Free Source: Tarable et al. paper Memory Banks time time 2

30 30 Broadcom Proprietary and Confidential. © 2013 Broadcom Corporation. All rights reserved. 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. 6-10, 2006 R GPP TSG RAN WG1 Meeting#47bis, Sorrento, Italy, Jan 15th-19th, 2007  QPP: ad-hoc contention-free mapping (Ericsson)

31 31 Broadcom Proprietary and Confidential. © 2013 Broadcom Corporation. All rights reserved. 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, Restriction: The number of parallel processors must be a divisor of the interleave size. 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, No restriction: Allows any possible number of parallel processors. 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*2 11. “Div” method needs at least 96 parallel processors. ‘Mod” method provides exactly 60 parallel processors. Previously existed Newly developed

32 32 Broadcom Proprietary and Confidential. © 2013 Broadcom Corporation. All rights reserved. CIRCULAR-BUFFER RATE MATCHING (PUNCTURING AND SHORTENING) Turbo Encoder SP1P2 Subblock Interleaver I Subblock Interleaver I Subblock Interleaver II Interleaved S Interleaved and interlaced P1 and P2 Circular buffer 3 rd TX 2 nd TX 1 st TX One code block Starting position 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 33 Broadcom Proprietary and Confidential. © 2013 Broadcom Corporation. All rights reserved. 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 34 Broadcom Proprietary and Confidential. © 2013 Broadcom Corporation. All rights reserved. DIGITAL VIDEO BROADCAST ( DVB ) SATELLITE SET-TOP BOX AND OTHERS LDPC CODES IN USE

35 35 Broadcom Proprietary and Confidential. © 2013 Broadcom Corporation. All rights reserved. LDPC CODE FOR DVB-S2, DVB-T2, AND DVB-C2 (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 (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). o Mitigates error floor (12 bits errors).  Inner Coding (LDPC).  Bit interleaving. o BICM (Bit-Interleaved Coded Modulation). QPSK w/o BCH w/BCH

36 36 Broadcom Proprietary and Confidential. © 2013 Broadcom Corporation. All rights reserved. DVB-S2 LDPC CODE DESIGN I: RA CODE 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 in Brest, France Tanner graph of RA code Accumulator

37 37 Broadcom Proprietary and Confidential. © 2013 Broadcom Corporation. All rights reserved. DVB-S2 LDPC CODES ARE IRA CODES k information bits b 0, b 1, …, b k Repetition: Every b i repeat r i times, i = 0,..., k-1 (bit degree distribution). Permutation: Interleave m = r 0 + r 1 +…+ r k-1 bits to generate y 0, y 1, …, y m-1. Accumulation: Generate parity bits (connect check equations). Final accumulation: p 0, p 1 = p 0 +p 1,…, p v = p v-1 +p v, …, p n-k-1 = p n-k-2 +p n-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 38 Broadcom Proprietary and Confidential. © 2013 Broadcom Corporation. All rights reserved. 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 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 The expanded matrix contains L permuted identity matrices, each one denoted as T u,v. VNU: Variable-node computation unit. CNU: Check-node computation unit H. Zhong and T. Zhang, T. “Design of VLSI Implementation-Oriented LDPC Codes,” The 58 th IEEE Vehicular Technology Conference, VTC Quasi-cyclic LDPC (QC-LDPC) code

39 39 Broadcom Proprietary and Confidential. © 2013 Broadcom Corporation. All rights reserved. DVB-S2 CODES ARE QC-LDPC Example: An IRA code with DVB-S2 permutation. Rate ½ (1248, 624) code. Two cyclic-shifted identity matrices on top of each other D 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

40 40 Broadcom Proprietary and Confidential. © 2013 Broadcom Corporation. All rights reserved.  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. DVB-S2 CODES ACHIEVEMENT Eroz, Sun, and Lee, “DVB-S2 low density parity check codes with near Shannon limit performance,” 2004

41 41 Broadcom Proprietary and Confidential. © 2013 Broadcom Corporation. All rights reserved. IS DVB-S2 LDPC CODE REALLY BETTER THAN TURBO CODE? Both LDPC decoder and Turbo decoder can be operated in parallel.

42 42 Broadcom Proprietary and Confidential. © 2013 Broadcom Corporation. All rights reserved. 10GBASE-T ETHERNET(IEEE 802.3AN) LDPC CODES IN USE

43 43 Broadcom Proprietary and Confidential. © 2013 Broadcom Corporation. All rights reserved. 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 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 44 Broadcom Proprietary and Confidential. © 2013 Broadcom Corporation. All rights reserved. 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. 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 45 Broadcom Proprietary and Confidential. © 2013 Broadcom Corporation. All rights reserved. SET-PARTITIONING USING CAPACITY APPROACHING CODE S 3,0 S 3,1 S 3,2 S 3,3 S 3,4 S 3,5 S 3,6 S 3,7 Δ L : Minimum intra-distance of S L,I, usually S L,i : A subset in level L (L-coded bits) Δ 0 : Minimum distance of the starting lattice 10*log 10 (2 L ) = 3*L dB set-partitioning. 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) Broadcom: IEEE P802.3an 10GBASE-T Task Force Code 4 bits per symbol.

46 46 Broadcom Proprietary and Confidential. © 2013 Broadcom Corporation. All rights reserved. 128 DSQ MAPPING (LABELING) Broadcom: IEEE P802.3an 10GBASE-T Task Force

47 47 Broadcom Proprietary and Confidential. © 2013 Broadcom Corporation. All rights reserved. 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 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(2 s )  GF * (2 s )={α i |i=-∞,0,1,…,2 s -2}, α -∞ =0,  Codeword size: ρ (≤2 s -1)  Minimum distance: ρ-1  Location mapping: α i → Z (α i ) = (0,…,0,1,0,…,0), a size 2 s vector, 1 at location i Regular LDPC matrix γ coset codes Tanner graph girth ≥ 6. Bit node degree =. Check node degree =. LDPC code d min

48 48 Broadcom Proprietary and Confidential. © 2013 Broadcom Corporation. All rights reserved. LDPC CODE SELECTION Final decision: GRS-based (2048,1723) code KeyEye T. Richardson “Error Floors of LDPC Codes” LDPC (1024,833) Broadcom Djurdjevic et. RS-based (2048,1732) LDPC code: d min = 8 Improved G and H matrices are defined in IEEE 802.3an spec.. Minimum distance calculations were provided by Marc Fossorier. Broadcom GRS -based (2048,1732): d min =14 IEEE P802.3an 10GBASE-T Task Force

49 49 Broadcom Proprietary and Confidential. © 2013 Broadcom Corporation. All rights reserved. WIRELESS LAN: Wi-Fi (IEEE ) LDPC CODES IN USE

50 50 Broadcom Proprietary and Confidential. © 2013 Broadcom Corporation. All rights reserved. LDPC CODE STRUCTURE FOR IEEE n 0 D D /2 2/3 3/4 5/6 0 D D Parity-Check matrices: CSI-SM based H = [H 1 H 0 ] H 0 corresponds to parity bits. 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 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 TGn Sync H0H0 WWiSE World Wide Spectrum Efficiency consortium H0H0 1/2 2/3 3/4 5/6

51 51 Broadcom Proprietary and Confidential. © 2013 Broadcom Corporation. All rights reserved. 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-ggn-k-g g LDPC matrix TGn SYNC H 0 = (1-0-1) is a nonsingular matrix. When 1 st part of check bits: 2 nd part of check bits: Information data:

52 52 Broadcom Proprietary and Confidential. © 2013 Broadcom Corporation. All rights reserved. Hughes Network Systems, STMicroelectronics, Texas Instruments and Trellisware: IEEE TGn AWGN WWiSE: IRA CODE STRUCTURE USED IN DVB-S2 0 D WWiSE Structure: IRA Code Column and row permuting (Used in DVB-S2) Better performance H0=H0= Redundancy-bit nodes Information-bit nodes Check nodes … … … Large open loop Tanner Graph

53 53 Broadcom Proprietary and Confidential. © 2013 Broadcom Corporation. All rights reserved. FINAL STRUCTURE Code constraints given by JP LDPC ad hoc group  H 0 uses “1-0-1” structure for RU encoding.  24 submatrices columns, submatrices size: 81,54, and 27 and maximal number of nonzero submatrices is LDPC codes (4 rates, 3 sizes) provided by Broadcom, Conexant, Hughes Network, Intel, Marvell, Motorola, Nokia, Nortel, STMicroelectronics, Texas Instruments, and Trellisware. 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 AWGN B TGn Channel

54 54 Broadcom Proprietary and Confidential. © 2013 Broadcom Corporation. All rights reserved. USAGE LDPC codes were never used in IEEE n production ac, 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 55 Broadcom Proprietary and Confidential. © 2013 Broadcom Corporation. All rights reserved. HOME NETWORK: MoCA 2.0 LDPC CODES IN USE

56 56 Broadcom Proprietary and Confidential. © 2013 Broadcom Corporation. All rights reserved. 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. 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. Broadcom: MoCA 2.0 F2F meeting

57 57 Broadcom Proprietary and Confidential. © 2013 Broadcom Corporation. All rights reserved. NARROWBAND (NB) INTERFERERS WILL SLIGHTLY REDUCE THE MAXIMUM PHY RATE Sub-carrier number dB Narrowband ingress noise with three Interferers 90% code 32 QAM AWGN 80% code 64 QAM AWGN 80% code 64 QAM (4.8b/s) NBI = 25 dBc 90% code 32 QAM(4.5b/s) NBI = 28 dBc 3 dBc difference x xx xx xx xx xx xxxxx xxxxx xxxx xxxxx xxxx xxxxx xxxxxx xxxxxx xxxxx xxxxx Broadcom 90% code structure  Irregular  Degree 6 bits in information  Degree 2 bits in parity parts Entropic 80% code structure  Regular  Degree 6 bits H0H0 H0H0

58 58 Broadcom Proprietary and Confidential. © 2013 Broadcom Corporation. All rights reserved. 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 59 Broadcom Proprietary and Confidential. © 2013 Broadcom Corporation. All rights reserved. MITIGATE NARROWBAND INGRESS NOISE (CONTINUED) 85% code structure  Regular in information  Low-triangular in parity x xx xxx xxxx xxxxx xxxxxx xxxxxxx An 85% code provides 0.5 dB spectral efficiency gain over an 80% code. 2.42dB 1.914dB MoCA 2.0 adopted the Broadcom 85% 4K LDPC code. Compare to RS Code (1024-QAM AWGN) An 85% code is short by 1 dB compared to an ENTR 80% code. (Narrow band ingress noise)

60 60 Broadcom Proprietary and Confidential. © 2013 Broadcom Corporation. All rights reserved. WIRELESS LAN: WiGig (IEEE ) LDPC CODES IN USE

61 61 Broadcom Proprietary and Confidential. © 2013 Broadcom Corporation. All rights reserved. WIGIG: IEEE AD 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 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: 1)Very high data rate 7 Gbps 2)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 62 Broadcom Proprietary and Confidential. © 2013 Broadcom Corporation. All rights reserved. REUSED LDPC CODE SET 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 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 merge

63 63 Broadcom Proprietary and Confidential. © 2013 Broadcom Corporation. All rights reserved. Three layers HIGH THROUGHPUT DECODING Parity-check matrix of C Layer decoding Source: M. Mansour and N. Shanbhag, Turbo decoder architectures for low-density parity-check codes Source: P. Radosavljevic, LDPC Decoding Algorithms & Implementation, Rice University 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 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.

64 64 Broadcom Proprietary and Confidential. © 2013 Broadcom Corporation. All rights reserved. COMBINING LAYER DECODING AND A REUSED CODE SET Column weight 1 per layer Reused Code Set Layer Decoding IEEE c high-rate wireless personal area networks (WPANs) The first proposal suggests using IEEE c LDPC code set. Column weight 1 per layer Row 1+row 2 Row 3+row 4

65 65 Broadcom Proprietary and Confidential. © 2013 Broadcom Corporation. All rights reserved. IT IS CHANNEL DEPENDENT AWGN Channel Fading Channel (Suitable for IEEE ad) c LDPC A call for introducing a new code set was made. (Key: high throughput and low-power decoding)

66 66 Broadcom Proprietary and Confidential. © 2013 Broadcom Corporation. All rights reserved. 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 Rate ½ Base Code In-place code set was adopted by IEEE ad Layer 1: 0+2, Layer 2: 1+3, Layer 3: 4+6, Layer 4: Rate 1/2 Rate 5/ Row Rate 3/4 Rate 13/16 Remove the first 2 rows Remove the first 1 rows

67 67 Broadcom Proprietary and Confidential. © 2013 Broadcom Corporation. All rights reserved. FULLY PARALLEL V. LAYER 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 68 Broadcom Proprietary and Confidential. © 2013 Broadcom Corporation. All rights reserved. CABLE MODEM LDPC CODES IN USE

69 69 Broadcom Proprietary and Confidential. © 2013 Broadcom Corporation. All rights reserved. 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. 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. 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 3.1 standard activity has not been publicly disclosed. EPoC IEEE 802.3bn task force is open to the public.

70 70 Broadcom Proprietary and Confidential. © 2013 Broadcom Corporation. All rights reserved. CODING PARTIAL BITS PER SYMBOL (SET-PARTITIONING) Six uncoded bits use 64-QAM mapping (Gray). Four coded bits use 16-QAM mapping (Gray) Broadcom: IEEE 802.3bn Task force Sept., dB 1.29 dB Partially coded FEC is more spectrally efficient and less complex QAM

71 71 Broadcom Proprietary and Confidential. © 2013 Broadcom Corporation. All rights reserved. IMPULSE NOISE IMPACT A burst of impulse noise may impact all subcarriers of one OFDM symbol or two consecutive OFDM symbols in one FEC frame. Cyclic prefix AWGN noise Burst duration One OFDM symbol SNR impulse One OFDM symbol 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 One burst impacted sub-carrier LDPC coded uncoded 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 Partial coded FEC Need another FEC code to protect uncoded bits

72 72 Broadcom Proprietary and Confidential. © 2013 Broadcom Corporation. All rights reserved. LDPC CODE FOP EPoC Burst Duration Burst SNRDVBC2 87.8%EPoC 89% 20 μs symbol (two affected) 16 μs20 dB μs μs 16 μs5 dB μs μs 40 μs symbol (two affected) 16 μs20 dB μs μs 16 μs5 dB μs μs Minimum depth and background SNR to achieve BER=1e-8 (4096-QAM, 30 iterations) EPoC (IEEE 802.3bn) accepted Broadcom LDPC code set as downstream and upstream FEC for FDD.  LDPC codes: o 8/9 (16200,14400) o 28/33 (5940,5040) o 3/4 (1120, 840)  No outer BCH code  Code all bits per symbol  No column-twisted bit interleaving (16200,14400) LDPC codes on 4096-QAM Broadcom: IEEE 802.3bn task force, July 2013

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