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Rilevamento e correzione degli errori

Codici CRC e codifica a blocchi e convoluzionale del canale

Applicare il rilevamento e la correzione degli errori utilizzando:

Tecniche di codifica con controllo a ridondanza ciclica (CRC). Sono inoltre compresi generatori e rilevatori CRC ottimizzati per HDL.
Tecniche di codifica a blocchi compresi i codici a blocchi lineari, i codici di Hamming, i codici Bose–Chaudhuri–Hocquenghem (BCH), i codici Reed-Solomon (RS), i codici a controllo di parità a bassa densità (LDPC) e i codici prodotto turbo (TPC). Sono inoltre compresi codificatori e decodificatori RS ottimizzati per HDL.
Tecniche di codifica convoluzionale comprese le tecniche convoluzionali, Turbo, di probabilità a posteriori (APP) e Viterbi. Sono inoltre compresi i decodificatori Turbo e Viterbi che possono essere eseguiti con le GPU per migliorare la velocità di elaborazione.
Campi di Galois per consentire la manipolazione di elementi di ordine pari e dispari dei campi finiti.

Per saperne di più sui codici di controllo degli errori, vedere Error Detection and Correction.

Funzioni

Codici di controllo a ridondanza ciclica

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

Codifica a blocchi

Codici a blocchi lineari

`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

Codici BCH

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

Codici Reed-Solomon

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

Codici LDPC

`ldpcEncode`	Encode binary LDPC code (Da R2021b)
`ldpcDecode`	Decode binary LDPC code (Da R2021b)
`ldpcEncoderConfig`	Create LDPC encoder configuration (Da R2021b)
`ldpcDecoderConfig`	Create LDPC decoder configuration (Da R2021b)
`ldpcQuasiCyclicMatrix`	Parity-check matrix of quasi-cyclic LDPC code (Da R2021b)
`dvbs2ldpc`	Low-density parity-check (LDPC) codes from DVB-S.2 standard

Codici prodotto Turbo

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

Codifica convoluzionale

`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 (Da R2021a)
`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

Campi di Galois

Calcoli nei campi di Galois - Campi finiti di ordine pari

`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

Campi di Galois a caratteristica dispari - Campi finiti di ordine dispari

`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

Oggetti

espandi tutto

Codici di controllo a ridondanza ciclica

`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

Codifica a blocchi

Codici BCH

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

Codici Reed-Solomon

`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

Codici LDPC

comm.gpu.LDPCDecoder (To be removed) Decode binary low-density parity-check (LDPC) code with GPU

Codifica convoluzionale

`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

Blocchi

espandi tutto

Codici di controllo a ridondanza ciclica

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

Codifica a blocchi

Codici a blocchi lineari

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

Codici BCH

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

Codici Reed-Solomon

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

Codici LDPC

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

Codici prodotto Turbo

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

Codifica convoluzionale

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

Argomenti

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.

Esempi in primo piano

DVB-S.2 Link, Including LDPC Coding

The application of low density parity check (LDPC) codes in the second generation Digital Video Broadcasting standard (DVB-S.2), which is deployed by DIRECTV in the United States. The example uses communications System objects to simulate a transmitter-receiver chain that includes LDPC encoding and decoding.

Apri script

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

The state-of-the-art channel coding scheme used in the second generation Digital Video Broadcasting standard (DVB-S.2), which is deployed by DIRECTV in the United States. The coding scheme is based on concatenation of LDPC (Low-Density Parity-Check) and BCH codes. LDPC codes, invented by Gallager in his seminal doctoral thesis in 1960, can achieve extremely low error rates near channel capacity by using a low-complexity iterative decoding algorithm. The outer BCH codes are used to correct sporadic errors made by the LDPC decoder.

Apri modello

LDPC Link Simulation Using GPU Processing

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

Apri live script

Parallel Concatenated Convolutional Coding: Turbo Codes

Characterize the performance of turbo codes over a noisy channel.

Apri modello

Tail-Biting Convolutional Coding

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

Apri script

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.

Apri live script

Punctured Convolutional Coding

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

Apri live script

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.

Apri live script

Using GPUs to Accelerate Turbo Coding Bit Error Rate Simulations

Use GPUs to dramatically accelerate bit error rate simulations.

Apri script

ElGamal Public Key Cryptosystem

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

Apri live script

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).

Apri script