NR Polar Decoder

Perform polar decoding according to 5G NR standard

Since R2020a

Libraries:
Wireless HDL Toolbox / Error Detection and Correction

Description

The NR Polar Decoder block implements a streaming polar decoder with hardware-friendly control signals. The 5G NR standard uses polar codes for channel coding of the DCI, UCI, and BCH transmit channels.

You must specify the link direction because the coding scheme defined by the 5G NR standard is different for downlink and uplink messages. Downlink messages are encoded with interleaving and use a CRC length of 24 bits. Uplink messages do not use interleaving, and use a CRC length of 6 or 11.

This block implements a CRC-aided successive-cancellation list decoder. This implementation matches the performance of the nrPolarDecode (5G Toolbox) function. You can choose a list length of 2, 4, or 8. Increasing the list length increases the error correction performance but uses more hardware resources and increases the decoding latency. You can improve decoding performance for DCI messages by using the optional RNTI port to specify an expected RNTI value.

This block also performs CRC decoding of the message, equivalent to the nrCRCDecode (5G Toolbox) function. The block selects the CRC length based on your specification of the link direction and the K value you provide. The block detects DCI messages from the values of K and E, and automatically prepends 1s to the message, equivalent to the padCRC input argument of the nrPolarDecode (5G Toolbox) function.

Because the latency of the polar decoding operation can vary, the block provides an output signal, nextFrame, that indicates when the block is ready to accept new inputs. For more details, see the Latency section of this page.

Examples

Polar Encode and Decode of Streaming Samples

Simulate NR Polar Encode and Decode blocks and compare the hardware-optimized results with results from 5G Toolbox™ functions.

Open Script

Ports

Input

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data — Input sample
scalar

Input sample, specified as a scalar log-likelihood ratio (LLR). The block supports builtin types, and signed fixed-point values with a wordlength of 4 to 16 bits.

The software supports double and single data types for simulation, but not for HDL code generation.

Data Types: fixed point | int8 | int16 | double | single

ctrl — Control signals accompanying sample stream
`samplecontrol` bus

Control signals accompanying the sample stream, specified as a samplecontrol bus. The bus includes the start, end, and valid control signals, which indicate the boundaries of the frame and the validity of the samples.

start — Indicates the start of the input frame
end — Indicates the end of the input frame
valid — Indicates that the data on the input data port is valid

For more details, see Sample Control Bus.

Data Types: bus

K — Length of information block in bits
positive integer

Length of information block in bits, specified as a positive integer. For downlink messages, K must be in the range 36 to 164. For uplink messages, K must be in the range 18 to 25 or 31 to 1023.

Dependencies

To enable this port, set the Configuration source parameter to Input port.

Data Types: fixdt(0,10,0)

E — Rate-matched output length in bits
scalar positive integer

Rate-matched output length in bits, specified as a scalar positive integer. Specify a value for E that is greater than K and less than or equal to 8192.

Dependencies

To enable this port, set the Configuration source parameter to Input port.

Data Types: fixdt(0,14,0)

RNTI — Target RNTI
16-bit unsigned integer

Target RNTI, specified as a 16-bit unsigned integer. This value increases decoding accuracy for DCI messages. For example, when decoding SIB1 DCI messages, enable this port and set the target RNTI to 65,535. For MIB decoding, you can disable this port or set the target RNTI to 0.

Dependencies

To enable this port, set Link direction to Downlink and select the Enable target RNTI port parameter.

Data Types: uint16

Output

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data — Decoded data bit
scalar

Decoded data bit, returned as a scalar. The output message length is A bits, where A = K – CRCLen. For downlink messages, CRCLen is 24. For uplink messages, CRCLen is 11 or 6, as defined by the 5G NR standard.

Data Types: fixdt(0,1,0) | Boolean | double | single
Complex Number Support: Yes

ctrl — Control signals accompanying sample stream
`samplecontrol` bus

Control signals accompanying the sample stream, returned as a samplecontrol bus. The bus includes the start, end, and valid control signals, which indicate the boundaries of the frame and the validity of the samples.

start — Indicates the start of the output frame
end — Indicates the end of the output frame
valid — Indicates that the data on the output data port is valid

For more details, see Sample Control Bus.

Data Types: bus

err — CRC result
scalar

CRC result, returned as a scalar. If you clear the Full checksum mismatch parameter, this value is a Boolean. When you select the Full checksum mismatch parameter, this value is a ufix24 scalar for downlink messages and a ufix11 or ufix6 scalar for uplink messages.

If you enable the RNTI port, the block compares the internal CRC checksum against the target RNTI value. Otherwise, the block compares the CRC checksum against a value of 0.

Data Types: Boolean | ufix11 | ufix24

nextFrame — Ready for new inputs
scalar

The block sets this signal to 1 when the block is ready to accept the start of the next frame. If the block receives an input start signal while nextFrame is 0, the block discards the frame in progress and begins processing the new data.

For more information, see Using the nextFrame Output Signal.

Data Types: Boolean

Parameters

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Link direction — Direction of 5G NR link
`Downlink` (default) | `Uplink`

Direction of 5G NR link, specified as Downlink or Uplink. When you choose Downlink, the block performs deinterleaving, as specified in the 5G NR standard. When you select Uplink, the block omits the deinterleaving logic.

Downlink decoding uses a CRC length of 24 bits. Uplink decoding uses a CRC length of 6 bits (K in the range 18 to 25) or 11 bits (K in the range 31 to 1023).

List length — Number of decoding paths
`2` (default) | `4` | `8`

This parameter is the maximum number of parallel paths maintained in the decoding tree. Increasing the list length increases the error correction performance but uses more hardware resources and increases the decoding latency. When you use list lengths of 4 and 8, the latency can vary depending on the SNR of the input signal, and is not constant for given values of K and E. Use the nextFrame output signal to determine when the block is available for a new message.

Configuration source — Source for K and E
`Property` (default) | `Input port`

Select Input port to enable the K and E ports. Select Property to use the Message length (K) and Rate-matched length (E) parameters.

Message length (K) — Length of information block in bits
`56` (default) | positive integer

For downlink messages, K must be in the range 36 to 164. For uplink messages, K must be in the range 18 to 25 or 31 to 1023.

Dependencies

To enable this parameter, set the Configuration source parameter to Property.

Rate-matched length (E) — Rate-matched output length in bits
`864` (default) | positive integer

Specify a value for E that is greater than K and less than or equal to 8192.

Dependencies

To enable this parameter, set the Configuration source parameter to Property.

Full checksum mismatch — Return checksum from final decoding stage
`off` (default) | `on`

When you clear this parameter, the block returns a Boolean scalar on the err port that indicates whether the CRC was successful. When you select this parameter, the block returns the full CRC checksum on the err port. If your design decodes DCI messages and makes use of the RNTI remainder, select this parameter.

If you enable the RNTI port, the block compares the internal CRC checksum with the target RNTI value. Otherwise, the block compares the CRC checksum against a value of 0.

The nrPolarDecode (5G Toolbox) function returns a decoded message that includes the CRC bits. This block returns the decoded message without the CRC bits, and returns the CRC status separately on the err port. This behavior is equivalent to calling the nrCRCDecode (5G Toolbox) function after using the nrPolarDecode function. Not recomputing the CRC bits saves hardware latency and resources.

Enable target RNTI port — Optional port to specify target RNTI value
`off` (default) | `on`

Select this parameter to enable the RNTI input port. Providing a target RNTI value increases decoding accuracy for DCI messages. For example, when decoding SIB1 DCI messages, enable this port and set the target RNTI to 65535. For MIB decoding, you can disable this port or set the target RNTI to 0.

Enabling this port also changes how the block computes the err output port value. If you enable the RNTI port, the block compares the internal CRC checksum with the target RNTI value. Otherwise, the block compares the CRC checksum against a value of 0.

Dependencies

To enable this parameter, set the Link direction parameter to Downlink.

Algorithms

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This block implements a CRC-aided successive-cancellation list decoder. It can use a list length of 2, 4, or 8 as configured by the List length parameter. The decoder iterates over all LLRs in the tree to reach a decision for a bit and then uses that decision to decode the next bit. The deinterleaving step is included only when you set the Link direction parameter to Downlink.

This diagram shows the architecture of the polar decoder.

The block uses the Configuration stage when the K and E input port values change. The block computes the locations of the information bits and passes them to the Decision stage. Because the mapping patterns are computed as needed, rather than stored in hardware, the block supports all K and E values within the supported range. The Configuration stage also computes the interleave pattern when you set the Link direction parameter to Downlink.

When you set the Configuration source parameter to Property, the K and E values are constants, so the decoder does not implement the Configuration stage. In this case, the block includes static lookup tables that contain the precomputed configuration.

To minimize computations for each decode, the Tree Memory stores the probability of each node being a one or a zero. Each iteration updates only the LLRs that have changed. The Core decoding stage uses the LLR update equations from [3].

The Decision stage checks the LLR value against the expected locations of information bits and frozen bits and returns a hard decision to the Tree Memory. If the bit is expected to be frozen, the Decision stage returns a hard decision of zero and updates the probabilities of related paths. The Path Memory reconstructs the most likely paths from the hard decision results and passes the paths and scores to the next stage.

Tree Memory and Path Memory contain up to List length paths. If all frozen bits on a path are zeros (as expected), then the block discards the other parallel paths. This optimization results in variable latency in the decoding operation for list lengths greater than two. For signals with a high noise level, the decoder must increase the number of parallel paths and the cycles for decoding. For low-noise signals, the decoder can use only two parallel paths and reduce the decoding latency.

The Path Selection stage computes the CRC for all paths and then chooses the path that passes the CRC. When you use the RNTI input port, the block compares the internal CRC checksum with the target RNTI value. Otherwise, the block compares the CRC checksum against a value of 0. If all CRCs fail, the block returns the path that has the higher score.

This implementation matches the performance of the 5G Toolbox™ function nrPolarDecode (5G Toolbox) with the same list length. Because the block uses fixed-point internal types, any differences are a result of quantization.

This plot shows the block error rate performance with the three possible list lengths. The input is 6-bit LLR values.

A plot showing the increase in performance for higher list lengths.

Latency

The table shows example latencies of the NR Polar Decoder block for each N, when decoding for uplink and downlink channels with a list length of two. N is the power-of-two encoded message length determined from the values of K and E.

N	Uplink Latency	Downlink Latency
32	349	Not applicable
64	576	677
128	1034	1135
256	1961	2062
512	3896	3996
1024	8202	Not applicable

The exact latency varies based on the values of K and E. The latency is longer for frames where the K and E input port values change and the block must compute the new configuration.

Increasing the list length increases the latency. List lengths greater than two do not have a fixed latency for given K and E values. To provide minimal latency, the block traces more than 2 paths only when the frozen bits are not decoded as zeroes. This optimization means that the latency can increase with the SNR of the input signal. For example, for a list length of 4 and N=512, the best case latency is 4108 cycles, and the worst case latency is 4985 cycles.

Because the latency varies, use the output nextFrame control signal to determine when the block is ready for a new input frame.

This waveform shows how the latency varies with the K and E input port values for a list length of two. When the input K and E port values are 132 and 256, the block has a latency of 2272 cycles from the input start signal to the output nextFrame. When the K and E port values change to 54 and 124, the latency changes to 1234 cycles.

This waveform shows how the latency can vary with the noise level of the input signal when using a list length of 4. The block has K and E parameter values of 132 and 256 and Link direction parameter set to Uplink. The first message has a latency of 2533 cycles. This message data is generated with low noise and has few bit errors. In this case, the decoder can collapse to two paths and produce a result in fewer cycles than when decoding a noisier signal. The second message is generated with a high noise level, and the decoding latency increases to 3174 cycles. When the input signal has more bit errors, the decoder must trace more paths to determine the correct bits.

Performance

This table shows the resource and performance data synthesis results of the block when it is configured with K and E as input ports, the Link direction parameter set to Downlink, and 6-bit input LLRs. The generated HDL is targeted to an AMD^® Zynq^®-7000 ZC706 evaluation board. The design achieves a clock frequency of 250 MHz.

Resource	List Length of 2	List Length of 4	List Length of 8
Slice LUTs	3048	4725	9963
Slice Registers	2509	3804	6471
DSP48	0	0	0
Block RAM	4.5	5.5	6.0

The block uses fewer resources when K and E are specified by parameters. When you set the Link direction parameter to Uplink, the block uses more memory to accommodate larger message sizes.

References

[1] 3GPP TS 38.212. "NR; Physical channels and modulation." 3rd Generation Partnership Project; Technical Specification Group Radio Access Network. URL: https://www.3gpp.org.

[2] Arikan, Erdal. "Channel Polarization: A Method for Constructing Capacity-Achieving Codes for Symmetric Binary-Input Memoryless Channels." IEEE Transactions on Information Theory 55, no. 7 (July 2009): 3051–73. https://doi.org/10.1109/TIT.2009.2021379.

[3] Balatsoukas-Stimming, Alexios, Mani Bastani Parizi, and Andreas Burg. "LLR-Based Successive Cancellation List Decoding of Polar Codes." IEEE Transactions on Signal Processing 63, no. 19 (October 2015): 5165–79. https://doi.org/10.1109/TSP.2015.2439211.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

This block supports C/C++ code generation for Simulink^® accelerator and rapid accelerator modes and for DPI component generation.

HDL Code Generation
Generate VHDL, Verilog and SystemVerilog code for FPGA and ASIC designs using HDL Coder™.

HDL Coder™ provides additional configuration options that affect HDL implementation and synthesized logic.

HDL Architecture

This block has one default HDL architecture.

HDL Block Properties

ConstrainedOutputPipeline	Number of registers to place at the outputs by moving existing delays within your design. Distributed pipelining does not redistribute these registers. The default is `0`. For more details, see ConstrainedOutputPipeline (HDL Coder).
InputPipeline	Number of input pipeline stages to insert in the generated code. Distributed pipelining and constrained output pipelining can move these registers. The default is `0`. For more details, see InputPipeline (HDL Coder).
OutputPipeline	Number of output pipeline stages to insert in the generated code. Distributed pipelining and constrained output pipelining can move these registers. The default is `0`. For more details, see OutputPipeline (HDL Coder).

Restrictions

You cannot generate HDL for this block inside a Resettable Synchronous Subsystem (HDL Coder).

Version History

Introduced in R2020a

NR Polar Decoder

Description

Examples

Polar Encode and Decode of Streaming Samples

Ports

Input

data — Input sample scalar

ctrl — Control signals accompanying sample stream samplecontrol bus

K — Length of information block in bits positive integer

Dependencies

E — Rate-matched output length in bits scalar positive integer

Dependencies

RNTI — Target RNTI 16-bit unsigned integer

Dependencies

Output

data — Decoded data bit scalar

ctrl — Control signals accompanying sample stream samplecontrol bus

err — CRC result scalar

nextFrame — Ready for new inputs scalar

Parameters

Link direction — Direction of 5G NR link Downlink (default) | Uplink

List length — Number of decoding paths 2 (default) | 4 | 8

Configuration source — Source for K and E Property (default) | Input port

Message length (K) — Length of information block in bits 56 (default) | positive integer

Dependencies

Rate-matched length (E) — Rate-matched output length in bits 864 (default) | positive integer

Dependencies

Full checksum mismatch — Return checksum from final decoding stage off (default) | on

Enable target RNTI port — Optional port to specify target RNTI value off (default) | on

Dependencies

Algorithms

Latency

Performance

References

Extended Capabilities

C/C++ Code Generation Generate C and C++ code using Simulink® Coder™.

HDL Code Generation Generate VHDL, Verilog and SystemVerilog code for FPGA and ASIC designs using HDL Coder™.

Version History

See Also

data — Input sample
scalar

ctrl — Control signals accompanying sample stream
`samplecontrol` bus

K — Length of information block in bits
positive integer

E — Rate-matched output length in bits
scalar positive integer

RNTI — Target RNTI
16-bit unsigned integer

data — Decoded data bit
scalar

ctrl — Control signals accompanying sample stream
`samplecontrol` bus

err — CRC result
scalar

nextFrame — Ready for new inputs
scalar

Link direction — Direction of 5G NR link
`Downlink` (default) | `Uplink`

List length — Number of decoding paths
`2` (default) | `4` | `8`

Configuration source — Source for K and E
`Property` (default) | `Input port`

Message length (K) — Length of information block in bits
`56` (default) | positive integer

Rate-matched length (E) — Rate-matched output length in bits
`864` (default) | positive integer

Full checksum mismatch — Return checksum from final decoding stage
`off` (default) | `on`

Enable target RNTI port — Optional port to specify target RNTI value
`off` (default) | `on`

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

HDL Code Generation
Generate VHDL, Verilog and SystemVerilog code for FPGA and ASIC designs using HDL Coder™.