错误检测和纠错

CRC 码以及分组编码和卷积信道编码

使用以下方法应用错误检测和纠错：

循环冗余校验 (CRC) 编码方法。还包括针对 HDL 优化的 CRC 生成器和检测器。
分组编码方法，包括线性分组码、汉明码、博斯-乔赫里-霍克文黑姆 (BCH) 码、里德-所罗门 (RS) 码、低密度奇偶校验 (LDPC) 码和 Turbo 乘积码 (TPC)。还包括针对 HDL 优化的 RS 编码器和解码器。
卷积编码方法，包括卷积、Turbo、后验概率 (APP) 和维特比方法。还包括可在 GPU 上运行以提高处理速度的 Turbo 和维特比解码器。
伽罗华域，以实现有限域中偶数和奇数阶元素的操作。

要了解有关错误控制码的更多信息，请参阅Error Detection and Correction。

函数

循环冗余校验码

`crcConfig`	Cyclic redundancy check (CRC) coding configuration (自 R2024a 起)
`crcGenerate`	Generate CRC code bits and append them to input data (自 R2024a 起)
`crcDetect`	Detect errors in input data using CRC parity bits (自 R2024a 起)

分组编码

线性分组码

`cyclgen`	Produce parity-check and generator matrices for cyclic code
`cyclpoly`	Produce generator polynomials for binary cyclic code
`decode`	Block decoder
`encode`	Block encoder
`gfweight`	Calculate minimum distance of linear block code
`gen2par`	Convert between parity-check and generator matrices
`hammgen`	Parity-check and generator matrices for Hamming code
`syndtable`	Produce syndrome decoding table

BCH 码

`bchenc`	BCH encoder
`bchdec`	BCH decoder
`bchgenpoly`	Produce generator polynomials for BCH code
`bchnumerr`	Number of correctable errors for BCH code

里德-所罗门码

`rsenc`	Reed-Solomon encoder
`rsdec`	Reed-Solomon decoder
`rsgenpoly`	Generator polynomial of Reed-Solomon code
`rsgenpolycoeffs`	Generator polynomial coefficients of Reed-Solomon code

LDPC 码

`ldpcEncode`	Encode binary LDPC code (自 R2021b 起)
`ldpcDecode`	Decode binary LDPC code (自 R2021b 起)
`ldpcEncoderConfig`	Create LDPC encoder configuration (自 R2021b 起)
`ldpcDecoderConfig`	Create LDPC decoder configuration (自 R2021b 起)
`ldpcPCM`	Generate parity-check matrix for LDPC coding (自 R2025a 起)
`ldpcQuasiCyclicMatrix`	Parity-check matrix of quasi-cyclic LDPC code (自 R2021b 起)

Turbo 乘积码

`tpcenc`	Turbo product code (TPC) encoder
`tpcdec`	Turbo product code (TPC) decoder

卷积编码

`convenc`	Convolutionally encode binary message
`vitdec`	Convolutionally decode binary data by using Viterbi algorithm
`distspec`	Compute distance spectrum of convolutional code
`getTurboIOIndices`	Compute output indices for turbo coding (自 R2021a 起)
`iscatastrophic`	True for trellis corresponding to catastrophic convolutional code
`istrellis`	True for valid trellis structure
`oct2dec`	Convert octal to decimal numbers
`poly2trellis`	Convert convolutional code polynomials to trellis description

伽罗华域

伽罗华域计算 - 偶数阶有限域

`convmtx`	Convolution matrix of Galois field vector
`cosets`	Produce cyclotomic cosets for Galois field
`dftmtx`	Discrete Fourier transform matrix in Galois field
`fft`	Fast Fourier transform of Galois field vector
`filter (gf)`	1-D digital filter over Galois field
`gf`	Galois field array
`gftable`	Generate file to accelerate Galois field computations
`ifft`	Inverse fast Fourier transform of Galois field vector
`isprimitive`	True for primitive polynomial for Galois field
`log`	Logarithm in Galois field
`minpol`	Find minimal polynomial of Galois field element
`mldivide`	Solve systems of linear equations Ax = B for x when A is a Galois array
`primpoly`	Find primitive polynomials for Galois field

奇特性伽罗华域 - 奇数阶有限域

`gfadd`	Add polynomials over Galois field
`gfconv`	Multiply polynomials over Galois field
`gfcosets`	Produce cyclotomic cosets for Galois field
`gfdeconv`	Divide polynomials over Galois field
`gfdiv`	Divide elements of Galois field
`gffilter`	Filter data using polynomials over prime Galois field
`gflineq`	Find particular solution of `Ax` = `b` over prime Galois field
`gfminpol`	Find minimal polynomial of Galois field element
`gfmul`	Multiply elements of Galois field
`gfpretty`	Polynomial in traditional format
`gfprimck`	Check whether polynomial over Galois field is primitive
`gfprimdf`	Provide default primitive polynomials for Galois field
`gfprimfd`	Find primitive polynomials for Galois field
`gfrank`	Compute rank of matrix over Galois field
`gfrepcov`	Convert one binary polynomial representation to another
`gfroots`	Find roots of polynomial over prime Galois field
`gfsub`	Subtract polynomials over Galois field
`gftrunc`	Minimize length of polynomial representation
`gftuple`	Simplify or convert Galois field element formatting

对象

全部展开

循环冗余校验码

`comm.CRCGenerator`	Generate CRC code bits and append to input data
`comm.CRCDetector`	Detect errors in input data using CRC
`comm.HDLCRCGenerator`	Generate CRC code bits and append to input data
`comm.HDLCRCDetector`	Detect errors in input data using CRC

分组编码

BCH 码

`comm.BCHEncoder`	Encode data using BCH encoder
`comm.BCHDecoder`	Decode data using BCH decoder

里德-所罗门码

`comm.RSEncoder`	Encode data using Reed-Solomon encoder
`comm.RSDecoder`	Decode data using Reed-Solomon decoder
`comm.HDLRSEncoder`	Encode message using Reed-Solomon encoder
`comm.HDLRSDecoder`	Decode message using Reed-Solomon decoder

卷积编码

`comm.ConvolutionalEncoder`	Convolutionally encode binary data
`comm.gpu.ConvolutionalEncoder`	Convolutionally encode binary data with GPU
`comm.TurboEncoder`	Encode input signal using turbo encoder parallel concatenated encoding scheme
`comm.APPDecoder`	Decode convolutional code by using APP method
`comm.TurboDecoder`	Decode input signal using turbo decoder parallel concatenated decoding scheme
`comm.gpu.TurboDecoder`	Decode input signal using turbo decoding with GPU
`comm.ViterbiDecoder`	Decode convolutionally encoded data using Viterbi algorithm
`comm.gpu.ViterbiDecoder`	Decode convolutionally encoded data using Viterbi algorithm with GPU

模块

全部展开

循环冗余校验码

General CRC Generator	Generate CRC code bits according to generator polynomial and append to input data frames
General CRC Syndrome Detector	Detect errors in received codeword frames according to generator polynomial
General CRC Generator HDL Optimized	Generate CRC code bits and append them to input data
General CRC Syndrome Detector HDL Optimized	Detect errors in input data using CRC

分组编码

线性分组码

Binary Cyclic Encoder	Create systematic cyclic code from binary vector data
Binary Cyclic Decoder	Decode systematic cyclic code to recover binary vector data
Binary Linear Encoder	Create linear block code from binary vector data
Binary Linear Decoder	Decode linear block code to recover binary vector data
Hamming Encoder	Create Hamming code from binary vector data
Hamming Decoder	Decode Hamming code to recover binary vector data

BCH 码

BCH Encoder	Create BCH code from binary vector data
BCH Decoder	Decode BCH code to recover binary vector data

里德-所罗门码

Binary-Input RS Encoder	Create Reed-Solomon code from binary vector data
Binary-Output RS Decoder	Decode Reed-Solomon code to recover binary vector data
Integer-Input RS Encoder	Create Reed-Solomon code from integer vector data
Integer-Output RS Decoder	Decode Reed-Solomon code to recover integer vector data
Integer-Input RS Encoder HDL Optimized	Encode data using a Reed-Solomon (RS) encoder
Integer-Output RS Decoder HDL Optimized	Decode data using Reed-Solomon (RS) decoder

LDPC 码

LDPC Encoder	Encode binary low-density parity-check (LDPC) code
LDPC Decoder	Decode binary low-density parity-check (LDPC) code

Turbo 乘积码

TPC Encoder	Turbo product code (TPC) encoder
TPC Decoder	Turbo product code (TPC) decoder

卷积编码

Convolutional Encoder	Encode binary data using convolutional encoding scheme
Turbo Encoder	Encode binary data using parallel concatenated encoding scheme
APP Decoder	Decode convolutional code using a posteriori probability (APP) method
Turbo Decoder	Decode input signal using parallel concatenated decoding scheme
Viterbi Decoder	Decode convolutionally encoded data using Viterbi algorithm

主题

Error Detection and Correction
Detect errors using cyclic redundancy check (CRC) codes. Learn about various error-control channel coding techniques.
Transmit and Receive Shortened Reed-Solomon Codes
Transmit and receive standard and shortened RS-encoded, 64-QAM-modulated data through an AWGN channel.
Reed-Solomon Coding with Erasures, Punctures, and Shortening in Simulink
Configure Reed-Solomon (RS) codes to perform block coding with erasures, punctures, and shortening.
Creation, Validation, and Testing of User Defined Trellis Structure
Use MATLAB^® to create and validate a user defined trellis structure, then use a unit test bench built in Simulink^® to test the implementation.
Working with Galois Fields
This example shows how to work with Galois fields.
Representation of Polynomials in Communications Toolbox
You can specify polynomials as a character vector or string scalar by using a variety of syntaxes.

精选示例

DVB-S.2 Link, Including LDPC Coding

Application of low density parity check (LDPC) codes in the second generation digital video broadcasting standard (DVB-S.2).

打开脚本

DVB-S.2 Link, Including LDPC Coding in Simulink

Model shows the channel coding scheme used in the second generation digital video broadcasting standard (DVB-S.2).

打开模型

LDPC Link Simulation Using GPU Processing

Use the ldpcDecode function and gpuArray to increase the speed of a communications system simulation.

打开实时脚本

Parallel Concatenated Convolutional Coding: Turbo Codes

Characterize the performance of turbo codes over a noisy channel.

打开模型

Tail-Biting Convolutional Coding

Use the Convolutional Encoder and Viterbi Decoder blocks to simulate a tail-biting convolutional code.

打开脚本

Rate 2/3 Convolutional Code in AWGN

Generate a bit error rate versus Eb/No curve for a link that uses 16-QAM modulation and a rate 2/3 convolutional code in AWGN.

打开实时脚本

Punctured Convolutional Coding

Use the convolutional encoder and Viterbi decoder System objects to simulate the bit error rate (BER) of a punctured coding system.

打开实时脚本

Estimate BER for Hard and Soft Decision Viterbi Decoding

Estimate bit error rate (BER) performance for hard-decision and soft-decision Viterbi decoders in AWGN. Compare the performance to that of an uncoded 64-QAM link.

打开实时脚本

Using GPUs to Accelerate Turbo Coding Bit Error Rate Simulations

Use GPUs to dramatically accelerate bit error rate simulations.

打开脚本

ElGamal Public Key Cryptosystem

Use the Galois field array function, gf, to implement an ElGamal public key cryptosystem.

打开实时脚本

5G LDPC Block Error Rate Simulation Using the Cloud or a Cluster

Use the cloud or a cluster for block error rate (BLER) simulation of low-density parity-check (LDPC) coding for the 5G NR downlink shared transport channel (DL-SCH).

打开脚本