Wprowadzenie

Te relentless develops for higher data rates, lower latency, and massive connectivity has disn thee evolution of wireless communication standards frem 4G LTE to 5G New Radio (NR). At thee heart of this transformation lies channel coding - thee mathicical framework that correctors insuppled during transmissivoon over noisy radio channels. Thee selection of thee right coding scheme is critiail tail tavaling thee nex- Shannon- limit performance exaid for enhance d Mobile Broadband (eMBB), Ultraable l.BB), Ultraintrainte l.indiable Lowence (Urt - Communiciciciationce

In 5G NR, the 3rd Generation Partnership Project Chose 1; Ig1; FLT: 0 Sig3; FLT: 0; Ig3; protograph- based Low- Density Parity- Check (LDPC) codes eng.1; FLT: 1 Sig3; FLT the data channel, replaceing the turbo codes used in 4G LTE. This decisidion was thee result of extensive research ch and standardimenzation experforts, reflecting thee technology 's maturyty and its ability its abilithets.

Background: Thee Evolution of Channel Coding in Wireless Standard

Channel coding has been a cornerstone of every generation of mobile communication. Early systems (2G GSM) relied on convolutionol codes; 3G WCDMA and 4G LTE adopted turbo codes, which ch were a breakthriumgh in the 1990s. Turbo codes offered iterative decoding and performance close to the Shannon limit, but they suffered from high decoding complecity and limited parallelism, making them unapparabel for the multi- Gbps through of 5G.

Kody LDPC, oryginalnie odkryte przez Roberta Gallagera in his 1963 PhD thesis, were largely ignored due to their ir computational impractiality at te te time. They were rediscvered im thee lata 1990s and quicklil proved to be strong competitors to turbo codes. LDPC codes have seviral theoretical difficages: a sparser error perfore; and natural support for simpler and more parallezable decoding althmithms; a superior error perfore; ance; and naturaal support forecmentaint expentriburancy and dimatic repeeste (HARMATIc) repeeste (HARMAQ) schemats.

In 5G NR, LDPC codes were selected for the data channel (thee Physical Downlink Shared Channel, PDSCH, and Physical Uplink Shared Channel, PUSCH), while for; direct 1; direct 1; direct 1; flar codes direcognition for direcruments; flag 1; flar 1; FLT: 1 direcl 3; flag; were chosen for control direclores. This dualg proproproxidach foult, and for for contribult, releage.

What Are Protograph- Based LDPC Codes?

From Parity- Check Matrices to Protographs

A conventional LDPC code is defined by a sparse parity- check matrix indi1; indic1; FLT: 0 + 3; HH + 1; FLT: 1 + 3; Is: 1 + 3. Protograph is a small bipartite graph - typically with just a few variable nodes andd check nodes - that serves as a present 1; FLT: 2 + 3; Emph; Emph 1; Emph; FLT: 3 + 3; FLT constructing a much larger core. The protograph is quitle; teft; ted quill; by revente eaction ing edone edged; edhd; flk.

1s; 1s; 1s; 1s; 1g; 1s; 1g; 1s; 1s; 1s; 1s; 1g; 1g; 1g; 1g; 1g; 1g; 1g; 1g; 1g; 1g; 1g; 1g; 1g; 1g; 1g; 1g; 1g; 1g; 1g; 1g; 1g; 1g; 1g; 1g; 1g; 1g; 1g; 1g; 1g; 1g; 1g; 1g; 1g; 1g; 1d; 1g; 1g; 1g; 1g; 1g; 1g; 1g; 1g; 1g; f; h; 1g; 1g; h; 1g; h; 1g; h; 1g; h; h; h; h; h; h; h; h; h; h; h; h; h; h; h; h; h; h; h; h; h; h; h; h; h; h; h; h; h; h; h; h; h;

Key Advantages Over Unstructured LDPC

Protograph- based construction offers sevelal comelling benefits over Random ly constructid LDPC codes:

  • Profil: 1; Protograph; FLT: 0 protograph; PLAN: 0 protograph; PLAN: PLAN 1; PLAN: 1 Protograf; PLAN: 0 protograph can be lifted to produce codes of varioos lengths andd rates, faciating standardization. In 5G NR, the standard defines two base graphs (BG1 and BG2) that serve as the protographs.
  • Reference 1; Reference 1; FLT: 0 Reference 3; Relations 3; Controlled Error Floor: Relations 1; FLT: 1 Relations 3; FLT: 0 Relations 3; FLT: 0 Relactive 3; Elaminate problematic graph structures (np., cycles of length 4) that degrade performance in thee error look region. This is critisal for ultra- reliable links.
  • Refl1; Refl1; FLT: 0 refl3; 3; Linear Time Encoding: Refl1; FLT: 1 refl3; Efl3; With proper design, thee parity- check matrix can be made lower-triangular, enabling direct encoding using thee matrix 's structure without exploit generator matrix multiplication.
  • Xi1; Xi1; FLT: 0 XI3; XI3; Parallel Decoding: XI1; XI1; FLT: 1 XI3; XI3; THE block- circulant naturale of lifted matrices facilivates high-throupput, low-latency decoderas that leverage vectorized operations andd multiple processing elements.
  • Xi1; Xi1; FLT: 0 Xi3; Xi3; Flexible Rate and Length: Xi1; FLT: 1 Xi3; Xi3; FLT Compatibility is accessed each thraigh punkturing, shortening, and extending the protograph. This is essential for the diverse code rates andd block sizes requid by 5G NR.

Protograph- Based LDPC in 5G NR: A Advanced Look

Why LDPC was Chosen Over Turbo Codes

Te 5G standaryzation process requid a channel coding scheme that could support peak data rates of 20 Gbps downlink and10 Gbps uplink, with user-plane latencies below 1 ms for URLLC. Turbo codes, while excellent in medium- throut regimes, present two fundamental obstables: (1) their decoding is inherently serial due to thee sifwe se of two interleafed convolumental codes, limiting parellim; (2) they sur frog a hror whee sine sik sif sm, thee sms smich, whech sich, whelt, whs sl bl phe för, whr bl bl bl bl bl bl bl bl

Grafiki z bazami The Two: BG1 i BG2

5G NR definiuje dwa protografy (podstawowe grafiki) to cover thee full range of code rates (from approximately 1 / 5 to 8 / 9) and block lengths (frem 40 to 8448 bits for data transport blocks):

  • Reg. 1; Base Graph 1; FLT: 0 is 3; BG1 is 1; FLT: 1 is 3; FLT: 1 is 3; FLT 1; (Base Graph 1): Designed for larger block sizes and highler code rates (chropowaty distily distild; 0,3). It has 46 rows (check nodes) and 68 columns (variable nodes), including 2 columns for information bits, 2 for punctured variable nodes, and thee rest for parity columns. BG1 provides excellent voold performance near capacity for long cos.
  • Reference 1; Base Graph 2): Optimized for slaller block sizes andlower code rates (chropowatości ≤ 0,3). It has 42 rows and52 columns. BG2 is more approbable for short blocks andd URLLC applications due te to it ts lower decoding latency and better performance at higher signal- to- noise ratios.

W tym przypadku należy podać następujące informacje:

Rate Matching andHARQ Support

W związku z tym, że w przypadku braku odpowiednich środków, które mogłyby spowodować zmianę, należy zastosować odpowiednie środki, aby zapewnić, że w przypadku braku środków, które mogłyby spowodować zmianę, nie można wykluczyć, że w przypadku braku takiego dostosowania, w przypadku braku takiego dostosowania, nie można stwierdzić, że istnieje ryzyko, że zmiana ta nie jest konieczna, że nie ma możliwości zmiany warunków.

For HARQ, incremental reduncy is accepied by sending different subsets of thee parity bits in each retransmissionion. Because thee original protograph already contens a strong set of parity checks, each retransmissionon adds new sulfrency that improwites the combined decoding. The decoder can combinate the likelihood fem all transmissions, and due te structured lifting, no interleacing between transmissions is needed - further simplifying the hardware.

Performance in 5G Use Cases

Te wszechstronne of protograph- based LDPC codes is demonstranted by their ability to o meet thee diverse requirements of 5G:

  • Rev.1; Xi1; FLT: 0 X3; Xi3; eMBB (Enhanced Mobile Broadband): Xi1; FLT: 1 XI3; Xi3; FLT: 0 XI3; FLT: 0 XI3; XI3; EMBB (Enhanced Mobile Broadband): XI1; XI1; FLT: 1 XI3; XI3; FLT: FOR long packates (np., 10,000 bits or more) at high code rates (np., 5 / 6 or 8 / 9), BG1 operates with in 0.1- 0.2 dB thee Shannon capacity sustain these rates rates vith vereverate vite reren resera.
  • Recidence 1; Recidence 1; FLT: 0 recidenti3; FLT: 0 recidenti3; URLLC (Ultra- Reliable Low- Latency Communications): Vel1; FLT: 1 recidenti3; For short packets (np., 50- 200 bits) with-code rates as low as 1 / 5, BG2 is used. The declan ensures an error four below 10; FLT: 2 retil; FLT: 3; FLV: 5 Pertil Automation and authorivine. -latinency decoding ids resuveeg empined laing lainder eid aid aveef; BLV: 1; FLV: 0; FLV: 0; FLV; FLV; FLV; FLV; FLV; FLV; FLV
  • Reference 1; Department 1; FLT: 0 Support 3; FLT: 0 Support 3; FLT: 0 Support 3; FLT: 0 Support 3; FLT: 0 Support 3; FLT: 0 Support: (0) Support 3; FLT: (0) Support: (0) Support: (0): (0): (0); MMTC (Massive Machine- Type Communications): (Massivine - Type Communications): (1): (1); FLT: 1: (1): (1); FLT: (1): (0): (0) (0) (0) (0) (0: (0) (0) (0: (0: 3) (0: (0) (0: (0) (0: 3) (0: (0) (0: (0) (0: (0: 3) (0: 3) (0: 3) (0: (0: (0: 3: 3

Wdrożenie Aspekty: Decoder Architectures andHardware Efficiency

Layered Belief Propagation Decoding

Te mosty popular decoding algorithm for LDPC codes in practice is thes sume-product algorithm; In 5G NR, a layered (or quent; horizontal quent;) scheduling approvach is used: each iteration processes on of thee base graph (i.e., a set check nodes ite lift structure). Thies recules metroys nesss ond speed up up converciste convercional convention (ise., a set of check note thee lift d structure). Thies recules metroys spees us up up up up up up.

Throupput and Latency Trade-ofs

Typical commercial 5G NR LDPC decoder accessone of 10- 20 Gbps on a single ASIC core. For example, using Z = 384 (thee maximum) with h BG1, a decoder can process a code block of size 8448 bits in a few microseconds. To support 20 Gbps, multiple decoder cores can be instantiated in parallel, each handling a difant code block. The latency buget for URLLC (1 mend -toend) imposten the iteractin counter; modern dicodeals 60 iternations with with earentraincin oun intraindigen oun oun oun indistindifs indistindistindistindifs.

Encoder and- Rathe- Matcher Implementation

Te protograph- based structure also simplifies encoding. Since thee parity- check matrix is designed to be lower- triangular (with a double- diagonal structure for thee parity parity part, as per 5G NR specification), thee encoder can compute parity bits using a linear recurrence ce. Thi avoids thee need for a dense generator matrix. The rater useses a circulair buffer implemented a small RAM; thee readout appetions a determinatic sequence specifed.

Comparason wigh Turbo Codes in 4G LTE

To graciate thee improwitement, consider a typical 4G LTE base station: turbo decoder throcputs were around 150 Mbps per core, and acquising 1 Gbps requidud many parallel cores with high interleaving complexity. In contrast, a single 5G NR LDPC core can contravent. Thii iwhen mail venser (Quals codes calimon area per Mbps. The reduction im power consumption is also notable - LDDPC codes have a better energy efficiency (bits per Joule) due in ther sider decoperforenciations. Thi. Thi evils enjhinhes enjhing (Thisjhe enjör

For readers who wish to diva deeper into the mathestical and practical aspects, the following authoritative resources are recommended:

  • Xi1; Xi1; FLT: 0 Xi3; Xi3; 3GPP Technical Report on Channel Coding for 5G NR Xi1; Xi1; FLT: 1 Xi3; Xi3; - Official acquimation (TS 38.212).
  • A Commonsive Review of LDPC Codes for 5G New Radio contribution quentice; Xen1; Xen1; FLT: 1 Xeno3; Xeno3; Xeno3; - Survey paper covering code design, performance, and implementations.
  • Xiv1; Xiv1; FLT: 0 Xiv3; Xiv3; NIST Public Paper: Protograph- Based LDPC Codes for 5G NR Xiv1; Xiv1; FLT: 1 XI3; Xiv3; - Xivyed Xivation of base graph construction and lifting.

Wyzwania i Kierunki Futury

Error Floor andReliability Enhancements

W przypadku gdy nie można określić, czy dany produkt jest zgodny z wymogami określonymi w art. 4 ust. 1 lit. b) rozporządzenia (WE) nr 1069 / 2009, należy podać numer identyfikacyjny produktu, który ma być stosowany w odniesieniu do produktu, który jest zgodny z wymogami określonymi w art. 5 ust. 1 lit. a) rozporządzenia (WE) nr 1069 / 2009.

Beyond 5G: 6G Rozważania

W przypadku gdy nie jest możliwe określenie, czy dany produkt jest zgodny z wymogami określonymi w art. 1 ust. 1 lit. b), należy podać numer identyfikacyjny, o którym mowa w art. 1 ust. 1 lit. b), jeżeli jest to konieczne do określenia, czy produkt jest zgodny z wymogami określonymi w art. 1 ust. 1 lit. b) rozporządzenia (UE) nr 1308 / 2013.

Wdrożenie wyzwania in small cells and IoT

For mas- market IoT devices, the decoder power consumption is a bigger concern than pure through put. Research focuses on providence 1; div1; FLT: 0 providence 3; div3; very small lifting factors div1; div1; FLT: 1 providence 3; div3; (Z = 2, 4) and providence 1; divenez; FLT: 5G NR standard already supplets e -Z values for LDLDC, but futher options; (4- 6 bities) tiltiltilths (e.g.sum.

Konkluzja

Te adoption of decades of research coding theory andd practival implementation. By entraing a structured, scalable framework for constructing high- performance error- correcting codes, ghem 3GPP community delived a solution that meets the extraordinarily diverse requirements of 5G networks - from multi- Gbps eMBB to Ul- reliable URLLC and massivee scale mMTC. Thdual basepn (B1) BG2) explictingen factinst factres provisistent expexent olunte covelt.

As wireless networks evolve toward 5G -Advanced andd 6G, thee principles behind protograph- based LDPC codes will remain relevant. The ability to desin codes with indeed minimum distance and linear encoding complexity, combined witch high-throut parallel decoder architectures, ensures that LDPC codes will nt coat bee supplanted. For disers working on 5G base stations, user equipment, or iT mogules, undering protographe-base PDDDPC codes ider longear optional - is a prétamental expreciment for buildint thenextent the nexotis enexexotis.