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Ba-Zhong Shen

Capacity-approaching channel coding in use. Ba-Zhong Shen. Communication and Information theory workshop (CITW2013) ,Oct. 14-18, 2013, Xi’an China. Data hungry world. Number of Users. OFDM. Transmission . Video Quality. High data rate . Modern Technology. High Demands. Capacity

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Ba-Zhong Shen

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  1. Capacity-approaching channel coding in use Ba-Zhong Shen Communication and Information theory workshop (CITW2013) ,Oct. 14-18, 2013, Xi’an China

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

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

  4. Ethernet (copper) 40 Gbps 10 Gbps IEEE 802.3y 100BASE-T2 1 Gbps IEEE 802.3i 10BASE-T twisted pair IEEE 802.3a 10BASE2 thinnet coax IEEE 802.3 10BASE5 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 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 7 Gbps 1 Gbps IEEE 802.11g (Better Ranges) IEEE 802.11a (OFDM) 150 Mbps (3 X 3 450) IEEE 802.11ad (WiGi,60 GHz) IEEE 802.11b (DSSS) Peak Data Rate IEEE 802.11ac 54 Mbps 54 Mbps IEEE 802.11 IEEE 802.11n (MIMO) 11 Mbps 2 Mbps

  7. Yesterday: Dominance of classical Channel coding

  8. Channel coding in previous standards

  9. Two mainly used classical channel coding methods QPSK Capacity 1bit/s/Hz Binary convolutional encoder used by IEEE 802.11. Uncoded 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. 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. 64 states Convolutional 8 states Convolutional Reed-Solomon Size 4608 Code rate 1/2 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 DOCSIS 3.0 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” Outer encoder inner encoder Interleave DVB-S, DOCSIS 3.0, VDSL and etc. used concatenated coding with RS outer code and trellis inner code

  13. Multidimensional TCM VDSL 2 Linear Combination and 4D Set-Partitioning 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. 2D-Constellation Modulation Convolutional Encoder 4D, 8D, or higher dimensional lattice partition. Transmit fractional information bits per carrier. 1000BASE-T

  14. Today: Capacity-approaching channel coding

  15. Turbo codes In 1993 ICC’93 Geneva, C.Berrou, A.Glavieux, and P. Thitimajshimtold 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. Turbo codes vs. TCM

  17. 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. 1995 Richardson, Shokrollahi, and Urbanke, IEEE –IT Vol. 42. No.2 2001

  18. LDPC code vs. RS and TCM concatenated codes 256-QAM

  19. LDPC code vs. concatenated code with 4-D trellis code Concatenated Rate 0.82 RS + 16-state 4D Wei TCM Rate 5/6 (0.83) G.Hn LDPC (5184,4320) 64-QAM SNR (dB)

  20. Satellite set-top box Turbo codes in use

  21. Turbo codes for satellite set-top boxes vN-1,1,…,v1,1,v0,1 0,…, 0 uN-M-1,1,…,u1,1,u0,1 Closure symbols generator Encoder Top(T) → t1,1,…tM,1, uN-M-1,1,…,u1,1,u0,1 0,…, 0 uN-M-1,0,…,u1,0,u0,0 vN-1,0,…,v1,0,v0,0 Mapper t1,0,…,tM,0, uN-M-1,0,…,u1,0,u0, Interleave Bottom(B) Encoder → 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. 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 Closure trellis within interleave block

  22. Achievement Rate ½ Codes QPSK 8-State Trellis Code 64-State Trellis Code Uncoded 1024-State Trellis Code 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 35percent in a given bandwidth or radio frequency link with no additional power requirements. … 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 • 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 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. 1/6 turbo encoder 3GPP2 C.S0024

  25. Turbo coding in 3GPP Universal Mobile Telecommunication System (UMTS)/WCDMA 3GPP TS 25.212, Release 6, 2005 Both Turbo encoder and interleaver are modified from CDMA2000. • 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 • Output of the encoder: x1, z1, z'1, x2, z2, z'2, … • xk never be punctured.

  26. Channel coding for LTE Channel Coding • Proposed schemes: • Turbo code • LDPC code • Criteria: • BLER ~1e-4 with HARQ • Simulation Results: • No significant difference 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. 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 , QPP: Quadratic Polynomial Permutation In this paper, a class of deterministicinterleaversfor Turbo codes (TCs) based on permutation polynomials over ZNis 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. 2005. where K is the information size. • LTE interleaver: QPP • Szes: 40 ~ 6144 • Total number of interleavers: 188 Motorola, R1-070056, 3GPP TSG-RAN WG1 #47bis, Jan. 2007

  28. Parallel Decoding

  29. Contention-free memory mapping Parallel decoding needs contention-free memory mapping. Processors @ time 1 Processors @ time 2 Processors @ time 2 Memory Banks Memory Banks Source: Tarable et al. paper 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.2002-2009, Sept. 2004 Contention-Free

  30. Fighting for surviving • Release 6 interleavers: ad-hoc contention-free mapping (Samsung, Nortel and Panasonic) R1-0632653GPP TSG RAN WG1 Meeting#47 Riga, Latvia, Nov. 6-10, 2006 • QPP: ad-hoc contention-free mapping (Ericsson) R1-0704633GPP TSG RAN WG1 Meeting#47bis, Sorrento, Italy, Jan 15th-19th, 2007

  31. Systematic Contention-free mappings for QPP 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. Previously existed Restriction: The number of parallel processors must be a divisor of the interleave size. Bank index Broadcom: R1-070618, 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–June29, 2007. Bank index Bit Index (before or after interleaving) Bit Index (before or after interleaving) Newly developed C|N with C > P and window size W ≥ N/P and gcd(W, C) = 1. 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*211. “Div” method needs at least 96 parallel processors. ‘Mod” method provides exactly 60 parallel processors.

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

  33. Rate matchingoptimization Broadcom “Rate matching proposal based on 15 period 8 optimal puncturing patterns,” R1-072542, 3GPP TSG RAN WG1 #49, Kobe, Japan, May 7th–11th, 2007.

  34. Digital video Broadcast（DVB） Satelliteset-top box and othersLDPC codes in use

  35. LDPC code for DVB-S2, DVB-T2, and DVB-C2 QPSK w/o 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). w/BCH

  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-1bits 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 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 DVB-S2 codes

  38. DVB-S2 LDPC code design II: hardware friendly 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. VNU: Variable-node computation unit. CNU:Check-node computation unit The expanded matrix contains L permuted identity matrices, each one denoted as Tu,v. 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) … 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. 2000. 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? 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 Robert M. Metcalfe (1973) 10GBASE-T/IEEE 802.3an Astandard 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, 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 128-Point “Doughnut” Constellation (Square) 128-Point Double Square Constellation (Square) KeyEye Proposed (Campopiano and Glazer 1962) Broadcom Proposed (Wei 1994) Teranetics Proposed Tomlinson-Harashimaprecoder(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-HarashimaPrecoders, “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 uncodedbits) (AWGN channel) S3,5 S3,2 S3,1 S3,6 S3,0 S3,4 S3,7 S3,3 Code 4 bits per symbol. SL,i: A subset in level L (L-coded bits) Δ0: Minimum distance of the starting lattice ΔL: Minimum intra-distance of SL,I, usually 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. LDPC code selection • 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 locationi Tanner graph girth ≥ 6. Bit node degree = . Check node degree = . LDPC code dmin RS Code-Based Regular LDPC Code Asimple 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 γcoset codes Regular LDPC matrix

  48. LDPC code selection LDPC (1024,833) T. Richardson “Error Floors of LDPC Codes” Broadcom KeyEye 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 Parity-Check matrices: CSI-SM based H = [H1 H0] H0 corresponds to parity bits. WWiSE World Wide Spectrum Efficiency consortium TGn Sync H0 H0 1/2 1/2 • The main objective of an IEEE 802.11n 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 2/3 2/3 3/4 3/4 5/6 5/6

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