A-law companders addition in Galois fields even number of field elements odd number of field elements algdeintrlv function algebraic interleavers algintrlv function algorithm objects properties specifying algorithm amdemod function ammod function analog modulation sample code analog signals representing analog-to-digital conversion arithdeco function arithenco function arithmetic codes parameters sample code arithmetic in Galois fields even number of field elements odd number of field elements AWGN channel awgn function baseband modulation signals BCH coding functions generator polynomial sample code using various coding methods bchdec function bchenc function bchgenpoly function berawgn function bercoding function berconfint function berfading function berfit function bersync function bertool function BERTool GUI data exporting importing in data viewer features MATLAB simulation BER confidence intervals curve fitting example stopping the simulation MATLAB simulation functions DPSK example QAM example requirements template parts of the GUI semianalytic BER example procedure Simulink BER example stopping the simulation Simulink models example requirements tips theoretical BER example types of systems bi2de function bin2gray function binary matrix format sample code binary numbers order of digits binary symmetric channel binary vector format sample code binary-to-decimal conversion bipolar random numbers bit error rates analyzing MATLAB simulation plots multiple curves semianalytic BERTool GUI simulation Simulink simulation theoretical BERTool GUI biterr function bits random block coding functions techniques block interleavers sample code supported methods Bose-Chaudhuri-Hocquenghem (BCH) coding functions generator polynomial sample code using various coding methods carrier frequency relative to sampling rate carrier signal channel objects copying creating in loop sample code properties linked realistic values repeatability resetting using channel visualization tool opening parts of the GUI plot (channel) StoreHistory using the GUI visualization options channels AWGN binary symmetric combination of fading and AWGN compensation for fading compensation for delays in loop realistic modeling parameters sample code supported types cma function code generator matrices converting to parity-check matrices sample code finding representing code generator polynomials finding representing codebooks optimizing for DPCM sample code sample code for DPCM representing codewords definition representing compand function companders sample code complex envelope compression data compressors sample code conjugate elements in Galois fields even number of field elements odd number of field elements constellations binary annotations decimal annotations Gray-coded general QAM square QAM hexagonal sample code plotting procedure PSK constraint length convolutional code convdeintrlv function convenc function conversion analog to digital binary to decimal binary to octal decimal to binary exponential to polynomial format even number of field elements odd number of field elements generator matrices to parity-check matrices sample code octal to decimal polynomial to exponential format even number of field elements odd number of field elements vectors to matrices convintrlv function convmtx function convolution over Galois fields convolutional coding adding to system binary symmetric channel examples features sample code using polynomial description sample code using trellis description convolutional interleavers delays sample code supported types correction vector cosets even number of field elements odd number of field elements cosets function cyclgen function cyclic coding functions generator polynomial sample code compared to generic linear coding for tracking errors using various coding methods cyclotomic cosets even number of field elements odd number of field elements cyclpoly function de2bi function decimal format sample code decision timing eye diagrams sample code for eye diagrams sample code for scatter plots decision-feedback equalizers decode function decoding tables deintrlv function delays adaptive equalizers convolutional interleavers fading channels MLSE equalizers delta modulation sample code See also differential pulse code modulation demodulation determinants in Galois fields even number of field elements dfe function dftmtx function differential pulse code modulation (DPCM) optimizing parameters sample code sample code digital modulation sample code step-by-step example digital signals representing discrete Fourier transforms over Galois fields distortion from DPCM from quantization distspec function division in Galois fields even number of field elements odd number of field elements Doppler shifts DPCM optimizing parameters sample code sample code dpcmdeco function dpcmenco function dpcmopt function dpskdemod function dpskmod function Eb/No encode function equalize function equalizer objects copying creating properties linked specifying algorithm using equalizers adaptive algorithms decision-directed mode decision-feedback delays fractionally spaced in loop procedure reference tap sample code basic procedure in loop training mode supported types symbol-spaced training mode equalizers, MLSE continuous operation delays preambles and postambles sample code continuous operation preamble error integers error patterns error rate plots curve fitting sample code multiple curves one curve error rates analyzing bit versus symbol MATLAB simulation sample code semianalytic BERTool GUI simulation Simulink simulation theoretical BERTool GUI theoretical results error-control coding adding to system base 2 only features of the toolbox methods supported in toolbox terminology and notation error-correction capability Hamming codes Es/No expanders sample code exponential format in Galois fields odd number of field elements exponentiation in Galois fields even number of field elements eye diagrams sample code eyediagram function factorization over Galois fields faded signals fading channels compensation for delays in loop realistic modeling parameters sample code feedback connection polynomials fft function fields, finite even number of elements odd number of elements filter function as a channel Galois fields filters fading channels Galois fields even number of field elements odd number of field elements Hilbert transform raised cosine designing designing and applying square-root raised cosine finite fields even number of elements odd number of elements flat fading fmdemod function fmmod function format of Galois field elements converting to exponential format even number of field elements odd number of field elements converting to polynomial format even number of field elements odd number of field elements even number of field elements odd number of field elements Fourier transforms over Galois fields fractionally spaced equalizers frequency-flat fading frequency-selective fading fskdemod function fskmod function Galois arrays creating manipulating variables meaning of integers in Galois fields even number of elements odd number of elements Gaussian channel Gaussian noise generating gen2par function general multiplexed interleaver generator matrices converting to parity-check matrices sample code finding representing generator polynomials finding for convolutional code representing genqamdemod function genqammod function gf function gfadd function gfconv function gfcosets function gfdeconv function gfdiv function gffilter function gflineq function gfminpol function gfmul function gfpretty function gfprimck function gfprimdf function gfprimfd function gfrank function gfrepcov function gfroots function gfsub function gftable function gftrunc function gftuple function gfweight function gray2bin function hammgen function Hamming coding functions sample code using various coding methods using various formats single-error-correction Hamming weight hank2sys function hard-decision decoding heldeintrlv function helical interleaver helical scan interleavers helintrlv function helscandeintrlv function helscanintrlv function Hilbert filters designing hilbiir function Huffman codes dictionary sample code huffmandeco function huffmandict function huffmanenco function ifft function intdump function integrate-and-dump operation interleavers block sample code supported methods convolutional delays sample code supported types intrlv function inverses in Galois fields even number of field elements odd number of elements irreducible polynomials iscatastrophic function isprimitive function istrellis function Jakes Doppler spectrum K-factor for Rician channels line-of-sight paths linear algebra in Galois fields even number of field elements linear block coding sample code linear predictors optimizing sample code representing lineareq function list of elements of Galois fields even number of field elements odd number of field elements generating Lloyd algorithm lloyds function lms function log function logarithms in Galois fields even number of field elements logical operations in Galois fields even number of field elements lowpass equivalent method marcumq function mask2shift function matdeintrlv function matintrlv function matrix interleavers matrix manipulation in Galois fields even number of field elements messages definition representing for coding functions minimal polynomials in Galois fields even number of field elements odd number of field elements minimum distance minpol function mldivide function MLSE equalizers continuous operation delays preambles and postambles sample code continuous operation preamble mlseeq function modnorm function modulation analog sample code delta sample code See also differential pulse code modulation digital sample code step-by-step example supported methods terminology Monte Carlo method for error-rate analysis mskdemod function mskmod function mu-law companders sample code multipath channels compensation for delays in loop realistic modeling parameters sample code multiple roots over Galois fields even number of field elements odd number of field elements multiplication in Galois fields even number of field elements odd number of field elements muxdeintrlv function muxintrlv function noisebw function noncausality normlms function Nyquist sampling theorem oct2dec function octal conversion from binary conversion to decimal optimizing DPCM parameters sample code quantization parameters sample code oqpskdemod function oqpskmod function order of digits in binary numbers pamdemod function pammod function parity-check matrices finding representing partitions optimizing for DPCM sample code sample code for DPCM representing passband modulation plot (channel) function pmdemod function pmmod function poly2trellis function polynomial description of encoders sample code polynomial format in Galois fields even number of field elements odd number of field elements polynomials displaying formatted generator polynomials over Galois fields arithmetic even number of field elements odd number of field elements binary coefficients evaluating even number of field elements even number of field elements irreducible minimal even number of field elements odd number of field elements odd number of field elements primitive. See primitive polynomials roots even number of field elements odd number of field elements postambles preambles sample code predictive error predictive order predictive quantization optimizing parameters sample code sample code predictors linear optimizing sample code representing primitive elements representing primitive polynomials consistent use default even number of field elements odd number of field elements definition even number of field elements odd number of field elements primpoly function pskdemod function pskmod function pulse shaping rectangular sample code punctured convolutional code qamdemod function qammod function qfunc function qfuncinv function quantiz function quantization coding DPCM parameters, optimizing sample code optimizing parameters sample code predictive sample code sample code vector quasi-static channel modeling raised cosine filters designing and applying designing but not applying filtering with sample code square-root randdeintrlv function randerr function randint function randintrlv function random bipolar symbols bits in error patterns integers signals symbols random interleavers randsrc function rank in Galois fields even number of field elements odd number of elements Rayleigh fading channels compensation for delays in loop realistic modeling parameters sample code rayleighchan function rcosfir function rcosflt function rcosiir function rcosine function rectangular pulse shaping rectpulse function Reed-Solomon coding functions generator polynomial references convolutional coding error-control coding Galois fields modulation/demodulation repeatability fading channels representing analog signals codewords decoding tables digital signals Galois field elements even number of field elements odd number of field elements Galois fields even number of field elements odd number of field elements generator matrices generator polynomials messages for coding functions parity-check matrices polynomials over Galois fields even number of field elements odd number of field elements predictors reset function for channels for equalizers Rician fading channels compensation for delays in loop realistic modeling parameters sample code ricianchan function rls function roots over Galois fields binary polynomials even number of field elements odd number of field elements rsdec function rsdecof function rsenc function rsencof function rsgenpoly function sampling rate relative to carrier frequency scalar quantization coding sample code scatter plots sample code scatterplot function semianalytic function semianalytic technique procedure sample code when to use shift2mask function signal constellations binary annotations decimal annotations Gray-coded square QAM hexagonal sample code plotting procedure PSK signal formatting signal sources signlms function simplifying formats of Galois field elements exponential odd number of field elements polynomial odd number of field elements simulation functions for BERTool sample code simulation of communication systems sample code Simulink models for BERTool SNR soft-decision decoding sample code solving linear equations over Galois fields source coding ssbdemod function ssbmod function subtraction in Galois fields even number of field elements odd number of field elements symbol error rates simulation symbol-spaced equalizers symerr function syndrome syndtable function theoretical error rates compared to empirical plots timing, decision eye diagrams sample code for eye diagrams sample code for scatter plots training data for optimizing DPCM quantization parameters for optimizing quantization parameters trellis description of encoder structure sample code truncating polynomials over Galois fields odd number of field elements varlms function vec2mat function vector quantization vitdec function waterfall curves curve fitting sample code multiple curves one curve weight, Hamming wgn function white Gaussian noise generating