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The Low Density Parity Check (LDPC) codes are powerful, capacity approaching channel codes and have exceptional error correction capabilities. The high degree of parallelism that they offer enables efficient, high throughput hardware architectures. The ntLDPC_WiFi6 IP Core is based on an implementation of QC-LDPC Quasi-Cyclic LDPC Codes and is fully compliant with IEEE 802.11 n/ac/ax standard. The Quasi-Cyclic LDPC codes are based on block-structured LDPC codes with circular block matrices. The entire parity check matrix can be partitioned into an array of block matrices; each block matrix is either a zero matrix or a right cyclic shift of an identity matrix. The parity check matrix designed in this way can be conveniently represented by a base matrix represented by cyclic shifts. The main advantage of this feature is that they offer high throughput at low implementation complexity. The ntLDPC_WiFi6 decoder IP Core may optionally implement one of two approximations of the log-domain LDPC iterative decoding algorithm (Belief propagation) known as either Layered Normalized Offset Min-Sum Algorithm or Layered Lambda-min Algorithm. Selecting between the two algorithms presents a decoding performance .vs. system resources utilization trade-off. The core is highly reconfigurable and fully compliant to the IEEE 802.11 n/ac/ax Wi-Fi4, Wi-Fi5 and Wi-Fi 6 standards. The ntLDPC_WiFi6 encoder IP implements a 81-bit parallel systematic LDPC encoder. An off-line profiling Matlab script processes the original matrices and produces a set of constants that are associated with the matrix and hardcoded in the RTL encoder.
In channel coding redundancy is inserted in the transmitted information bit-stream. This redundant information is used in the decoder to eliminate the channel noise. The error correction capability of a FEC system strongly depends on the amount of redundancy as well as on the coding algorithm itself. TPCs perform well in the moderate to high SNRs because the effect of error floor is less. As TPCs have more advantage when a high rate code is used, they are suitable for commercial applications in wireless and satellite communications. The ntTPC Turbo Product Codec IP core is consisted of the Turbo Product Encoder (ntTPCe) and the Turbo Product Decoder (ntTPCd) blocks. The product code C is derived from two/three constituent codes, namely C1, C2 and optionally C3. The information data is encoded in two/three dimensions. Every row of C is a code of C2 and every column of C is a code of C1. When the third coding dimension is enabled, then there are C3 C1*C2 data planes. The ntTPC core supports both e-Hamming and Single Parity Codes as the constituent codes. The core also supports shortening of rows or columns of the product table, as well as turbo shortening. Shortening is a way of providing more powerful codes by removing information bits from the code. The ntTPCe core receives the information bits row by row from left to right and transmits the encoded bits in the same order. It consists of a row, column and 3D encoder. The ntTPCd decoder receives soft information from the channel in the 2’s complement number system and the input samples are received row by row from left to right. The implemented decoding algorithm computes the extrinsic information for every dimension C1, C2, C3 by iteratively decoding words that are near the soft-input word. An advanced scalable and parametric design approach produces custom design versions tailored to end customer applications design tradeoffs.
The ntLDPC_DVBS2X IP Core is based on an implementation of QC-LDPC Quasi-Cyclic LDPC Codes. These LDPC codes are based on block-structured LDPC codes with circular block matrices. The entire parity check matrix can be partitioned into an array of block matrices; each block matrix is either a zero matrix or a right cyclic shift of an identity matrix. The parity check matrix designed in this way can be conveniently represented by a base matrix represented by cyclic shifts. The main advantage of this feature is that they offer high throughput at low implementation complexity. The ntLDPC_DVBS2X decoder IP Core may optionally implement one of two approximations of the log-domain LDPC iterative decoding algorithm (Belief propagation) known as either Layered Offset Min-Sum Algorithm or Layered Lambda-min Algorithm. Selecting between the two algorithms presents a decoding performance .vs. system resources utilization trade-off. The core is highly reconfigurable and fully compliant to the DVB-S2 and DVB-S2X standards. Two highly complex off-line preprocessing series of procedures are performed to optimize the DVB LDPC parity check matrices to enable efficient RTL implementation. The ntLDPC_DVBS2X encoder IP implements a 360-bit parallel systematic LDPC IRA encoder. An off-line profiling Matlab script processes the original IRA matrices and produces a set of constants that are associated with the matrix and hardcoded in the RTL encoder. Actual encoding is performed as a three part recursive computation process, where row sums, checksums of all produced rows column-wise and finally transposed parity bit sums are calculated. The ntLDPC_DVBS2X decoder IP implements a 360-bit parallel systematic LDPC layered decoder. Two separate off-line profiling Matlab series of scripts are used to (a) process the original IRA matrices and produce the layered matrices equivalents (b) resolve any possible conflicts produced by the layered transformation. The decoder IP permutes each block’s parity LLRs to become compatible with the layered decoding scheme and stores channel LLRs to processes them in layered format. Each layer corresponds to 360 expanded rows of the original LDPC matrix. Each layer element corresponds to the active 360x360 shifted identity submatrices, within a layer. Each layer element is shifted accordingly and processed by the parallel decoding datapath unit.
The ntLDPC_5GNR Base Graph Encoder IP Core is defined in 3GPP TS 38.212 standard document and it is based on an implementation of QC-LDPC Quasi-Cyclic LDPC Codes. The specification defines two sets of LDPC Base Graphs and their respective derived Parity Check Matrices. Each Base Graph can be combined with 8 sets of lifting sizes (Zc) in a total of 51 different lifting sizes. This way by using the 2 Base Graphs, the 5G NR specification defines up to 102 possible distinct LDPC modes of operation to select from, for optimum decoding performance, depending on target application code block size and code rate (using the additional rate matching module features). For Base Graph 1 we have LDPC(N=66xZc,K=22xZc) sized code blocks, while for Base Graph 2 we have LDPC(N=50xZc,K=[6,8,9,10]xZc) sized code blocks. The ntLDPCE_5GNR Encoder IP implements a multi-parallel systematic LDPC encoder. Parallelism depends on the selected lifting sizes subsets chosen for implementation. Shortened blocks are supported with granularity at lifting size Zc-bit boundaries. Customizable modes generation is also supported beyond the scope of the 5G-NR specification with features such as: “flat parity bits puncturing instead of Rate Matching Bit Selection”, “maintaining the first 2xZc payload bits instead of eliminating it before transmission”, etc. The ntLDPCD_5GNR decoder IP implements a maximum lifting size of Zc_MAX-bit parallel systematic LDPC layered decoder. Each layer corresponds to Zc_MAX expanded rows of the original LDPC matrix. Each layer element corresponds to the active ZcxZc shifted identity sub-matrices within the layer. Each layer element is shifted accordingly and processed by the parallel decoding datapath unit, in order to update the layers LLR estimates and extrinsic information iteratively until the required number of decoding iterations has been run. The decoder IP also features a powerful optional early termination (ET) criterion, to maintain practically equivalent error correction performance, while significantly increasing its throughput rate and/or reducing hardware cost. Additionally it reports how many decoding iterations have been performed when ET is activated, for system performance observation and calibration purposes. Finally a simple, yet robust, flow control handshaking mechanism is included in both IPs, which is used to communicate the IPs availability to adjacent system components. This logic is easily portable into any communication protocol, like AXI4 stream IF.
The ntLDPC_8023CA (17664,14592) IP Core is defined in IEEE 802.3ca-2020 standard document and it is based on an implementation of QC-LDPC Quasi-Cyclic LDPC Codes. These LDPC codes are based on block-structured LDPC codes with circular block matrices. The entire parity check matrix can be partitioned into an array of block matrices; each block matrix is either a zero matrix or a right cyclic shift of an identity matrix. The parity check matrix designed in this way can be conveniently represented by a base matrix represented by cyclic shifts. The main advantage of this feature is that they offer high throughput at low implementation complexity. The ntLDPCE_8023CA encoder IP implements a 256-bit parallel systematic LDPC encoder. The Generator LDPC Matrix is calculated off-line, compressed and stored in ROM. It is partitioned to 12 layers and each layer when multiplied by the 14592 payload block pro-duces 256 parity bits. The multiplier architecture may be parameterized before synthesis to generate multiple multiplier instances [1 to 6], in order to effectively process multiple layers in parallel and improve the IP throughput rate. Shortened blocks are supported with granularity of 128-bit boundaries and 384 or 512 parity bits puncturing is also optionally supported. The ntLDPCD_8023CA decoder IP Core may optionally implement one of two approximations of the log-domain LDPC iterative decoding algorithm (Belief propagation) known as either Layered Offset Min-Sum Algorithm (OMS) or Layered Lambda-min Algorithm (LMIN). Selecting between the two algorithms presents a decoding performance vs system resources utilization trade-off. The OMS algorithm is chosen for this implementation, given the high code rate of the Parity Check Matrix (PCM). The ntLDPCD_8023CA decoder IP implements a 256-bit parallel systematic LDPC layered decoder. Each layer corresponds to Z=256 expanded rows of the original LDPC matrix. Each layer element corresponds to the active ZxZ shifted identity sub-matrices within the layer. Each layer element is shifted accordingly and processed by the parallel decoding datapath unit, in order to update the layers LLR estimates and extrinsic information iteratively until the required number of decoding iterations has been run. The decoder IP also features a powerful optional early termination (ET) criterion, to maintain practically equivalent error correction performance, while significantly increasing its throughput rate and/or reducing hardware cost. Additionally it reports how many decoding iterations have been performed when ET is activated, for system performance observation and calibration purposes. Finally a simple, yet robust, flow control handshaking mechanism is included in both IPs, which is used to communicate the IPs availability to adjacent system components. This logic is easily portable into any communication protocol, like AXI4 stream IF.
ntLDPC_SDAOCT IP implements a 5G-NR Base Graph 1 systematic Encoder/Decoder based on Quasi-Cyclic LDPC Codes (QC-LDPC), with lifting size Zc=384 and Information Block Size 8448 bits. The implementation is based on block-structured LDPC codes with circular block matrices. The entire parity check matrix can be partitioned into an array of block matrices; each block matrix is either a zero matrix or a right cyclic shift of an identity matrix. The parity check matrix designed in this way can be conveniently represented by a base matrix represented by cyclic shifts. The main advantage of this feature is that it offers high throughput at low implementation complexity. The ntLDPCE_SDAOCT Encoder IP implements a systematic LDPC Zc=384 encoder. Input and Output may be selected to be 32-bit or 128-bits per clock cycle prior to synthesis, while internal operations are 384-bits parallel per clock cycle. Depending on code rate, the respective amount of parity bits are generated and the first 2xZc=768 payload bits are discarded. There are 5 code rate modes of operation available (8448,8448)-bypass, (9984,8448)-0.8462, (11136,8448)-0.7586, (12672,8448)-0.6667 and (16896,8448)-0.5. The ntLDPCD_SDAOCT Base Graph Decoder IP may optionally implement one of two approximations of the log-domain LDPC iterative decoding algorithm (Belief propagation) known as either Layered Min-Sum Algorithm (MS) or Layered Lambda-min Algorithm (LMIN). Variations of Layered MS available are Offset Min-Sum (OMS), Normalized Min-Sum (NMS), and Normalized Offset Min-Sum (NOMS). Selecting between these algorithms presents a decoding performance vs. system resources utilization trade-off. The ntLDPCD_SDAOCT decoder IP implements a Zc=384 parallel systematic LDPC layered decoder. Each layer corresponds to Zc=384 expanded rows of the original LDPC matrix. Each layer element corresponds to the active ZcxZc shifted identity submatrices within the layer. Each layer element is shifted accordingly and processed by the parallel decoding datapath unit, in order to update the layers LLR estimates and extrinsic information iteratively until the required number of decoding iterations has been run. The decoder IP also features a powerful optional early termination (ET) criterion, to maintain practically equivalent error correction performance, while significantly increasing its throughput rate and/or reducing hardware cost. Additionally it reports how many decoding iterations have been performed when ET is activated, for system performance observation and calibration purposes. Finally a simple, yet robust, flow control handshaking mechanism is included in both IPs, which is used to communicate the IPs availability to adjacent system components. This logic is easily portable into any communication protocol, like AXI4 stream IF.
The ntRSC_DP1.4 IP core is compliant with Display Port 1.4 standard as published by Video Electronics Standards Association (VESA) for use in DSC (Display Stream Compression) technology. It is based on Reed-Solomon RS(254,250), 10 bit symbols, forward error correction code, where the codeword block consists of 250 information symbols and 4 RS parity symbols. The ntRSC_DP1.4 FEC IP Core ensures error resilient / glitch-free compressed video transport (DSC) to external displays. The implementation is very low latency, high speed with a simple interface for easy integration in SoC applications.
The ntLDPC_G98042 (17664,14592) IP Core is defined in IEEE 802.3ca-2020, it is used by ITU-T G.9804.2-09.2021 standard document and it is based on an implementation of QC-LDPC Quasi-Cyclic LDPC Codes. These LDPC codes are based on block-structured LDPC codes with circular block matrices. The entire parity check matrix can be partitioned into an array of block matrices; each block matrix is either a zero matrix or a right cyclic shift of an identity matrix. The parity check matrix designed in this way can be conveniently represented by a base matrix represented by cyclic shifts. The main advantage of this feature is that they offer high throughput at low implementation complexity. The ntLDPCΕ_G98042 encoder IP implements a 256-bit parallel systematic LDPC encoder. The Generator LDPC Matrix is calculated off-line, compressed and stored in ROM. It is partitioned to 12 layers and each layer, when multiplied by the 14592 payload block, produces 256 parity bits. The multiplier architecture may be parameterized before synthesis to generate multiple multiplier instances [1:4,6], in order to effectively process multiple layers in parallel and improve the IP throughput rate. Shortened blocks are supported with granularity of 128-bit boundaries and 384 or 512 parity bits puncturing is also optionally supported. The ntLDPCD_G98042 decoder IP Core may optionally implement one of two approximations of the log-domain LDPC iterative decoding algorithm (Belief propagation) known as either Layered Offset Min-Sum Algorithm (OMS) or Layered Lambda-min Algorithm (LMIN). Selecting between the two algorithms presents a decoding performance vs. system resources utilization trade-off. The OMS algorithm is chosen for this implementation, given the high code rate of the Parity Check Matrix (PCM). The ntLDPCD_G98042 decoder IP implements a 256-bit parallel systematic LDPC layered decoder. Each layer corresponds to Z=256 expanded rows of the original LDPC matrix. Each layer element corresponds to the active ZxZ shifted identity sub-matrices within the layer. Each layer element is shifted accordingly and processed by the parallel decoding datapath unit, in order to update the layers’ LLR estimates and extrinsic information iteratively until the required number of decoding iterations has been run. The decoder IP also features a powerful optional syndrome check early termination (ET) criterion, to maintain identical error correction performance, while significantly increasing its throughput rate and/or reducing hardware cost. Additionally it reports how many decoding iterations have been performed when ET is activated, for system performance observation and calibration purposes. A top level architecture deployment wrapper allows to expand the parallelism degree of the decoder before synthesis, effec-tively implementing a trade-off between utilized area and throughput rate. Finally a simple, yet robust, flow control handshaking mechanism is included in both IPs, which is used to communicate the IPs availability to adjacent system components at 128-bit parallel bus interface. This logic is easily portable into any communication protocol, like AXI4 stream IF.
Convolutional FEC codes are very popular because of their powerful error correction capability and are especially suited for correcting random errors. The most effective decoding method for these codes is the soft decision Viterbi algorithm. ntVIT core is a high performance, fully configurable convolutional FEC core, comprised of a 1/N convolutional encoder, a variable code rate puncturer/depuncturer and a soft input Viterbi decoder. Depending on the application, the core can be configured for specific code parameters requirements. The highly configurable architecture makes it ideal for a wide range of applications. The convolutional encoder maps 1 input bit to N encoded bits, to generate a rate 1/N encoded bitstream. A puncturer can be optionally used to derive higher code rates from the 1/N mother code rate. On the encoder side, the puncturer deletes certain number of bits in the encoded data stream according to a user defined puncturing pattern which indicates the deleting bit positions. On the decoder side, the depuncturer inserts a-priori-known data at the positions and flags to the Viterbi decoder these bits positions as erasures. The Viterbi decoder uses a maximum-likelihood detection recursive process to cor-rect errors in the data stream. The Viterbi input data stream can be composed of hard or soft bits. Soft decision achieves a 2 to 3dB in-crease in coding gain over hard-decision decoding. Data can be received continuously or with gaps.
ntRSD core implements a time-domain Reed-Solomon decoding algorithm. The core is parameterized in terms of bits per symbol, maximum codeword length and maximum number of parity symbols. It also supports varying on the fly shortened codes. Therefore any desirable code-rate can be easily achieved rendering the decoder ideal for fully adaptive FEC applications. ntRSD core supports erasure decoding thus doubling its error correction capability. The core also supports continuous or burst decoding. The implementation is very low latency, high speed with a simple interface for easy integration in SoC applications.
ntRSD_UF core implements a time-domain Reed-Solomon decoding algorithm. The core is parameterized in terms of bits per symbol, maximum codeword length, maximum number of parity symbols as well as I/O data width, internal datapath and decoding engines parallelism. It also supports varying on the fly shortened codes. Therefore any desirable code-rate can be easily achieved rendering the decoder ideal for fully adaptive FEC applications. ntRSD_UF core supports erasure decoding thus doubling its error correction capability. The core also supports continuous or burst decoding. The core is designed and optimized for applications that need very high throughput data rates. The implementation is very low latency, high speed with a simple interface for easy integration in SoC applications.
The ntLDPC_Ghn IP Core is based on an implementation of QC-LDPC Quasi-Cyclic LDPC Codes. These LDPC codes are based on block-structured LDPC codes with circular block matrices. The entire parity check matrix can be partitioned into an array of block matrices; each block matrix is either a zero matrix or a right cyclic shift of an identity matrix. The parity check matrix designed in this way can be conveniently represented by a base matrix represented by cyclic shifts. The main advantage of this feature is that they offer high throughput at low implementation complexity. The ntLDPCD_Ghn decoder IP Core may optionally implement one of two approximations of the log-domain LDPC iterative decoding algorithm (Belief propagation) known as either Layered Offset Min-Sum Algorithm or Layered Lambda-min Algorithm. Selecting between the two algorithms presents a decoding performance .vs. system resources utilization trade-off. The core is highly reconfigurable and fully compliant to the ITU-T G.9960 G.hn standard. The ntLDPCE_Ghn encoder IP implements a 360-bit parallel systematic LDPC encoder. An off-line profiling Matlab script processes the original matrices and produces a set of constants that are associated with the matrix and hardcoded in the RTL encoder. The ntLDPCD_Ghn decoder IP implements a 360-LLR parallel systematic LDPC layered decoder. A separate off-line profiling Matlab script is used to profile the layered matrices and resolve any possible memory access conflicts. Each layer corresponds to Z=[14, 80, 360, 60, 270, 48 or 216] expanded rows of the original LDPC matrix, depending on the mode selected expansion factor. Each layer element corresponds to the active ZxZ shifted identity sub-matrices, within a layer. Each layer element is shifted accordingly and processed by the parallel decoding datapath unit, in order to update the layers LLR estimates and extrinsic information iteratively until the required number of decoding iterations has been executed. The decoder also IP features a powerful optional early termination (ET) criterion, to maintain practically the same error correction performance, while significantly increasing its throughput rate. Additionally it reports how many decoding iterations have been performed when ET is activated, for system performance observation and calibration purposes. Finally a simple, yet robust, flow control handshaking mechanism is included in both IPs, which is used to communicate the IPs availability to adjacent system components. This logic is easily portable into any communication protocol, like AXI.
ntRSE core implements the Reed Solomon encoding algorithm and is parameterized in terms of bits per symbol, maximum codeword length and maximum number of parity symbols. It also supports varying on the fly shortened codes. Therefore any desirable code-rate can be easily achieved rendering the decoder ideal for fully adaptive FEC applications. ntRSE core supports continuous or burst decoding. The implementation is very low latency, high speed with a simple interface for easy integration in SoC applications.
ntRSC_IESS core is a highly integrated solution implementing a time-domain Reed-Solomon Forward Error Correction algorithm. The core supports several programming features including codeword size, error threshold, number of parity bytes, reverse or forward order of the output, mode of operation (encode, decode or pass-through), shortened code support, erasures or error only decoding. Very low latency, high speed, simple interfacing and programmability make this core ideal for many applications including Intelsat IESS-308, DTV, DBS, ADSL, Satellite Communications, High performance modems and networks.
The ntDVBS2_FEC transmitter and receiver IPs, each instantiate an outer BCH and inner LDPC concatenated pair of encoders and decoders respectively. The Bose, Chaudhuri, and Hocquenghem (BCH) codes are the largest category of the powerful error-correction cyclic codes and belong to the block codes that are a generalization of the Hamming codes for multiple-error corrections. The Low Density Parity Check (LDPC) codes are powerful, capacity approaching channel codes and have exceptional error correction capabilities. The high degree of parallelism that they offer enables efficient, high throughput hardware architectures. The concatenation of these two error correction algorithms enable performance well close to the Shannon limit. The ntBCH_DVBS2 encoder performs BCH encoding to payload frames by appending calculated parity bits at the end of each frame. The ntBCH_DVBS2 decoder finds the error locations within a received frame, tries to correct them and indicates a successful or failed decoding procedure. The ntLDPC_DVBS2 IP Core is based on an implementation of QC-LDPC Quasi-Cyclic LDPC Codes. These LDPC codes are based on block-structured LDPC codes with circular block matrices. The entire parity check matrix can be partitioned into an array of block matrices; each block matrix is either a zero matrix or a right cyclic shift of an identity matrix. The parity check matrix designed in this way can be conveniently represented by a base matrix represented by cyclic shifts. The main advantage of this feature is that they offer high throughput at low implementation complexity. The ntLDPC_DVBS2 encoder IP implements a 360-bit parallel systematic LDPC IRA encoder. An off-line profiling Matlab script processes the original IRA matrices and produces a set of constants, associated with the matrix and hardcoded in the RTL encoder. Encoding is performed as a three part recursive computation process, where row sums, checksums of all rows column-wise and parity bit sums are calculated. The ntLDPC_DVBS2 decoder IP implements an approximation of the log-domain LDPC iterative decoding algorithm (Belief propagation), known as Layered Lambda-min2 Algorithm. The core is highly reconfigurable in terms of area, throughput and error correction performance trade-offs and is fully compliant to the DVB-S2 standard. Two highly complex off-line preprocessing series of procedures are performed to optimize the DVB LDPC parity check matrices to enable efficient RTL implementation. The ntLDPC_DVBS2 decoder IP implements a 360-LLR parallel systematic LDPC layered decoder. Two separate off-line profiling Matlab series of scripts are used to (a) process the original IRA matrices and produce the layered matrices equivalents (b) resolve any possible conflicts produced by the layered transformation. Each layer corresponds to 360 expanded rows of the original LDPC matrix. Each layer element corresponds to the active 360x360 shifted identity sub-matrices, within a layer. Each layer element is shifted accordingly and processed by the parallel decoding datapath unit, in order to update the layers LLR estimates and extrinsic information iteratively until the required number of decoding iterations has been run. The decoder also IP features two powerful optional early termination (ET) criteria (convergence and parity check), to maintain practically the same error correction performance, while significantly increasing its throughput rate. Additionally it reports how many decoding iterations have been performed when ET is activated, for system performance observation and calibration purposes. Finally a simple, yet robust, flow control hand-shaking mechanism is included in both IPs, which is used to communicate the IPs availability to adjacent system components. This logic is easily portable into any communication protocol, like AXI.
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