# C Program For Convolutional Code Matlab Pattern

Description decoded = vitdec(code,trellis,tblen, opmode, dectype) decodes the vector code using the Viterbi algorithm. The MATLAB ® structure trellis specifies the convolutional encoder that produced code; the format of trellis is described in and the reference page for the function. Code contains one or more symbols, each of which consists of log2(trellis.numOutputSymbols) bits. Each symbol in the vector decoded consists of log2(trellis.numInputSymbols) bits. Tblen is a positive integer scalar that specifies the traceback depth. If the code rate is 1/2, a typical value for tblen is about five times the constraint length of the code.

Opmode indicates the decoder's operation mode and its assumptions about the corresponding encoder's operation. Choices are in the table below. Value Meaning 'cont' The encoder is assumed to have started at the all-zeros state. The decoder traces back from the state with the best metric. A delay equal to tblen symbols elapses before the first decoded symbol appears in the output. This mode is appropriate when you invoke this function repeatedly and want to preserve continuity between successive invocations. See the below.

'term' The encoder is assumed to have both started and ended at the all-zeros state, which is true for the default syntax of the convenc function. The decoder traces back from the all-zeros state. This mode incurs no delay. This mode is appropriate when the uncoded message (that is, the input to convenc) has enough zeros at the end to fill all memory registers of the encoder. If the encoder has k input streams and constraint length vector constr (using the polynomial description of the encoder), “enough” means k*max(constr-1). 'trunc' The encoder is assumed to have started at the all-zeros state. The decoder traces back from the state with the best metric.

Han Introduction to Binary Convolutional Codes 2 Encoders for the Convolutional Codes 1. A binary convolutional encoder is conveniently structured as a.

This mode incurs no delay. This mode is appropriate when you cannot assume the encoder ended at the all-zeros state and when you do not want to preserve continuity between successive invocations of this function. For the 'term' and 'trunc' mode, the traceback depth ( tblen) must be a positive integer scalar value, not greater than the number of input symbols in code. Dectype indicates the type of decision that the decoder makes, and influences the type of data the decoder expects in code. Choices are in the table below.

Syntax for Punctures and Erasures decoded =. Vitdec(code,trellis,tblen, opmode, dectype,puncpat) denotes the input punctured code, where puncpat is the puncture pattern vector, and where 0s indicate punctured bits in the input code.

Vitdec(code,trellis,tblen, opmode, dectype,puncpat,eraspat) allows an erasure pattern vector, eraspat, to be specified for the input code, where the 1s indicate the corresponding erasures. Eraspat and code must be of the same length. If puncturing is not used, specify puncpat to be [].

In the eraspat vector, 1s indicate erasures in the input code. Additional Syntaxes for Continuous Operation Mode Continuous operation mode enables you to save the decoder's internal state information for use in a subsequent invocation of this function. Repeated calls to this function are useful if your data is partitioned into a series of smaller vectors that you process within a loop, for example. Vitdec(.,' cont'.,initmetric,initstates,initinputs) is the same as the earlier syntaxes, except that the decoder starts with its state metrics, traceback states, and traceback inputs specified by initmetric, initstates, and initinputs, respectively.

Each real number in initmetric represents the starting state metric of the corresponding state. Initstates and initinputs jointly specify the initial traceback memory of the decoder; both are trellis.numStates-by- tblen matrices. Initstates consists of integers between 0 and trellis.numStates-1. If the encoder schematic has more than one input stream, the shift register that receives the first input stream provides the least significant bits in initstates, while the shift register that receives the last input stream provides the most significant bits in initstates. The vector initinputs consists of integers between 0 and trellis.numInputSymbols-1. To use default values for all of the last three arguments, specify them as [],[],[].

[decoded,finalmetric,finalstates,finalinputs] =. Vitdec(.,' cont'.) is the same as the earlier syntaxes, except that the final three output arguments return the state metrics, traceback states, and traceback inputs, respectively, at the end of the decoding process.

Finalmetric is a vector with trellis.numStates elements that correspond to the final state metrics. Finalstates and finalinputs are both matrices of size trellis.numStates-by- tblen. The elements of finalstates have the same format as those of initstates. Traceback Matrices The t th column of P 1 shows the t-1 th time step states given the inputs listed in the input matrix.

For example, the value in the i th row shows the state at time t-1 that transitions to the i-1 state at time t. The input required for this state transition is given in the i th row of the t th column of the input matrix. The P 1 output is the states of the traceback matrix. It is a [number of states x traceback length] matrix. The following example uses a (7,5), rate 1/2 code.

This code is easy to follow: t = poly2trellis(3,[7 5]); k = log2(t.numInputSymbols); msg = [1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0]; code = convenc(msg,t); tblen = 15; [d1 m1 p1 in1]=vitdec(code(1:end/2),t,tblen,'cont','hard'). In1 = 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 In this example, the message makes the encoder states follow the following sequence: 0 2 3 1 / 0 2 3 1 /. Since the best state is 0 (column index of smallest metric in m 1 –1), the traceback matrix starts from sate 0, looking at the first row ( 0 th state) of the last column of P 1, ([1; 3; 1; 3]), which is 1. This indicates 1 for the previous state.

Next, the traceback matrix checks in1 ([0; 0; 1; 1]), which indicates 0 for the input. The second row (1st state) of the 14 th column of P 1 ([1; 3; 1; 3]) is 3. This indicates 3 for the previous state. The traceback matrix checks in1 ([0; 0; 1; 1]), which indicates that the input was 0. The fourth row (3rd state) of the 13th column of P 1 ([0; 2; 0; 2]), is 2.

E Prime Serial Number Crack For Fl. This indicates 2 for the previous state. The traceback matrix checks in1 ([0; 0; 1; 1]), which indicates the input was 1. The third row (2nd state) of the 12th column of P 1 ([0; 2; 0; 2]), is 0. This indicates 0 for the previous state. The traceback matrix checks in1 ([0; 0; 1; 1]), which indicates the input was 1.

The first row (0th state) of the 11th column of P 1 ([1; 3; 1; 3]), is 1. This indicates 1 for the previous state. Then, the matrix checks in1 ([0; 0; 1; 1]), which indicates 0 for the input. To determine the best state for a gicen time, use m 1.

The smallest number in m 1 represents the best state. For n = 1:length(EbNoVec)% Convert Eb/No to SNR snrdB = EbNoVec(n) + 10*log10(k*rate);% Reset the error and bit counters [numErrsSoft,numErrsHard,numBits] = deal(0); while numErrsSoft.

This is our exercise in image processing homework. My code is working fine. I would like to get some help with code optimization. Function C = convolve_slow(A,B) (file name is accordingly convolve_slow.m ) This routine performs convolution between an image A and a mask B. Input: A - a grayscale image (values in [0,255]) B - a grayscale image (values in [0,255]) serves as a mask in the convolution.

Output: C - a grayscale image (values in [0,255]) - the output of the convolution. C is the same size as A. Method: Convolve A with mask B using zero padding. Assume the origin of B is at floor(size(B)/2)+1. Do NOT use matlab convolution routines (conv,conv2,filter2 etc). Make the routine as efficient as possible: Restrict usage of for loops which are expensive (use matrix multiplications and matlab routines such as dot etc).

To simplify and reduce ifs, you should pad the image with zeros before starting your convolution loop. Do not assume the size of A nor B (B might actually be larger than A sometimes). Here is our solution function [ C ] = convolve_slow( A,B )%This routine performs convolution between an image A and a mask B.% Input: A - a grayscale image (values in [0,255])% B - a grayscale image (values in [0,255]) serves as a mask in the convolution.% Output: C - a grayscale image (values in [0,255]) - the output of the convolution.% C is the same size as A.%% Method: Convolve A with mask B using zero padding. Assume the origin of B is at floor(size(B)/2)+1.% init C to size A with zeros C = zeros(size(A));% make b xy-reflection and vector vectB = reshape(flipdim(flipdim(B,1),2)',[], 1);% padding A with zeros paddedA = padarray(A, [floor(size(B,1)/2) floor(size(B,2)/2)]);% Loop over A matrix: for i = 1:size(A,1) for j = 1:size(A,2) startAi = i; finishAi = i + size(B,1) - 1; startAj = j; finishAj = j + size(B,2) - 1; vectPaddedA = reshape(paddedA(startAi:finishAi,startAj:finishAj)',1,[]); C(i,j) = vectPaddedA* vectB; end end end since i'm new to Image Processing and Matlab.

Can you please help me with code optimization, specifically with matrix based operations. Is it possible not to use loops? Without writing the code out explicitly, I can see a way to get it down to one main for loop. Basically, think of the matrix A and B as column vectors by unwrapping each column of A and B into a vector (that's how it's stored internally in MATLAB).

Then each (i,j) coordinate of A can be mapped to a linear index k (using the function sub2ind for example). Then, for each linear index within the body of A (ignoring padding), compute the list of linear indices corresponding the a submatrix around this linear index (that's probably the hardest part here). Then compute the dot product of A( theseIndices ) and B(:).

With this method you are just looping over each linear index of A.

Introduction This example showcases the simulation of a communication system consisting of a random binary source, a convolutional encoder, a BPSK modulator, an additive white Gaussian noise (AWGN) channel, and a Viterbi decoder. The example shows how to run simulations to obtain bit error rate (BER) curves and compares these curves to a theoretical bound. Initialization Convolutional Encoding with Puncturing Create a rate 1/2, constraint length 7 System object. This encoder takes one-bit symbols as inputs and generates 2-bit symbols as outputs. If you assume 3-bit message words as inputs, then the encoder will generate 6-bit codeword outputs. ConvEncoder = comm.ConvolutionalEncoder(poly2trellis(7, [171 133])); Specify a puncture pattern to create a rate 3/4 code from the previous rate 1/2 code using the puncture pattern vector [1;1;0;1;1;0]. The ones in the puncture pattern vector indicate that bits in positions 1, 2, 4, and 5 are transmitted, while the zeros indicate that bits in positions 3 and 6 are punctured or removed from the transmitted signal.

The effect of puncturing is that now, for every 3 bits of input, the punctured code generates 4 bits of output (as opposed to the 6 bits produced before puncturing). This results in a rate 3/4 code. In the example at hand, the length of the puncture pattern vector must be an integer multiple of 6 since 3-bit inputs get converted into 6-bit outputs by the rate 1/2 convolutional encoder. To set the desired puncture pattern in the convolutional encoder System object, hConvEnc, set the PuncturePatternSource property to Property and the PuncturePattern property to [1;1;0;1;1;0].

BpskMod = comm.BPSKModulator; Create an System object. Set the NoiseMethod property of the channel to Signal to noise ratio (Eb/No) to specify the noise level using the energy per bit to noise power spectral density ratio (Eb/No).

When running simulations, test the coding system for different values of Eb/No ratio by changing the EbNo property of the channel object. The output of the BPSK modulator generates unit power signals; set the SignalPower property to 1 Watt. The system at hand is at the symbol rate; set the SamplesPerSymbol property to 1. VitDecoder = comm.ViterbiDecoder(poly2trellis(7, [171 133]).

'InputFormat', 'Unquantized'); In general, the puncture pattern vectors you use for the convolutional encoder and Viterbi decoder must be the same. To specify the puncture pattern, set the PuncturePatternSource property of the Viterbi decoder System object, hVitDec, to Property. Set the PuncturePattern property to the same puncture pattern vector you use for the convolutional encoder. Because the punctured bits are not transmitted, there is no information to indicate their values. As a result, the decoding process ignores them. VitDecoder.PuncturePatternSource = 'Property'; vitDecoder.PuncturePattern = convEncoder.PuncturePattern; For a rate 1/2 code with no puncturing, you normally set the traceback depth of a Viterbi decoder to a value close to 40. Decoding punctured codes requires a higher value, in order to give the decoder enough data to resolve the ambiguities that the punctures introduce.

This example uses a traceback depth of 96. Set this value using the TraceBackDepth property of the Viterbi decoder object, hVitDec. VitDecoder.TracebackDepth = 96; Calculating the Error Rate Create an calculator System object to compare decoded bits to the original transmitted bits. The output of the error rate calculator object is a three-element vector containing the calculated bit error rate (BER), the number of errors observed, and the number of bits processed. The Viterbi decoder creates a delay in the output decoded bit stream equal to the traceback length.

To account for this delay set the ReceiveDelay property of the error rate calculator System object to 96. ErrorCalc = comm.ErrorRate( 'ReceiveDelay', vitDecoder.TracebackDepth); Stream Processing Loop Analyze the BER performance of the punctured coding system for different noise levels. Uncoded and Coded Eb/No Ratio Values Typically, you measure system performance according to the value of the energy per bit to noise power spectral density ratio (Eb/No) available at the input of the channel encoder. The reason for this is that this quantity is directly controlled by the systems engineer. Analyze the performance of the coding system for Eb/No values between 2 and 5 dB. BERVec = zeros(3,length(EbNoEncoderOutput));% Allocate memory to store results for n=1:length(EbNoEncoderOutput) reset(errorCalc) reset(convEncoder) reset(vitDecoder) channel.EbNo = EbNoEncoderOutput(n);% Set the channel EbNo value for simulation while (BERVec(2,n).

In some cases, at lower bit error rates, simulation results appear to indicate error rates slightly above the bound. This results from simulation variance (if fewer than 500 bit errors are observed) or from the finite traceback depth in the decoder. Summary We utilized several System objects to simulate a communications system with convolutional coding and puncturing.

We simulated the system to obtain BER performance versus different Eb/No ratio values. The BER results were compared to theoretical bounds. Selected Bibliography.