Simulation Source Code Examples-Tutorial on Convolutional Coding with Viterbi Decoding-Simulation Source Code Examples Read about how the family of Chinese prime minister Wen JiaBao enriched themselves by as much as US$2.7 Billion during his tenure as leader on the New York Times website: If you're behind the so-called 'Great Firewall,' try the BBC News website: or the Washington Post website: You can also try to read the pdf version in Chinese: Simulation Source Code Examples The simulation source code comprises a test driver routine and several functions, which will be described below. This code simulates a link through an AWGN channel from data source to Viterbi decoder output. The first dynamically allocates several arrays to store the source data, the convolutionally encoded source data, the output of the AWGN channel, and the data output by the Viterbi decoder. It calls the data generator, convolutional encoder, channel simulation, and Viterbi decoder functions in turn. It then compares the source data output by the data generator to the data output by the Viterbi decoder and counts the number of errors. Once 100 errors (sufficient for +/- 20% measurement error with 95% confidence) are accumulated, the test driver displays the BER for the given Es/No. The test parameters are controlled by definitions in.
FPGA Implementation of Viterbi Algorithm for Decoding of Convolution Codes K.Santhosh Kumar1. Aditya Institute of Technology And Management, India) Abstract: Convolutional code is a coding scheme used in communication systems including deep space. Since the Viterbi algorithm is implemented as a program, which is executed by the.
The test driver includes a compile-time option to also measure the BER for an uncoded channel, i.e. A channel without forward error correction. I used this option to validate my Gaussian noise generator, by comparing the simulated uncoded BER to the theoretical uncoded BER given by, where E b/N 0 is expressed as a ratio, not in dB. I am happy to say that the results agree quite closely. When running the simulations, it is important to remember the relationship between E s/N 0 and E b/N 0.
As stated earlier, for the uncoded channel, E s/N 0 = E b/N 0, since there is one channel symbol per bit. However, for the coded channel, E s/N 0 = E b /N 0 + 10log 10(k/n).
For example, for rate 1/2 coding, E s/N 0 = E b/N 0 + 10log 10(1/2) = E b/N 0 - 3.01 dB. For rate 1/8 coding, E s/N 0 = E b/N 0 + 10log 10(1/8) = E b/N 0 - 9.03 dB. The function simulates the data source. It accepts as arguments a pointer to an input array and the number of bits to generate, and fills the array with randomly-chosen zeroes and ones.
The function accepts as arguments the pointers to the input and output arrays and the number of bits in the input array. It then performs the specified convolutional encoding and fills the output array with one/zero channel symbols. The convolutional code parameters are in the header file. The function accepts as arguments the desired E s/N 0, the number of channel symbols in the input array, and pointers to the input and output arrays. It performs the binary (one and zero) to baseband signal level (+/- 1) mapping on the convolutional encoder channel symbol outputs. It then adds Gaussian random variables to the mapped symbols, and fills the output array.
The output data are floating point numbers. The arguments to the function are the expected E s/N 0, the number of channel symbols in the input array, and pointers to its input and output arrays. First, the decoder function sets up its data structures, the arrays described in the algorithm description section. Then, it performs three-bit soft quantization on the floating point received channel symbols, using the expected E s/N 0, producing integers. (Optionally, a fixed quantizer designed for a 4 dB E s/N 0 can be chosen.) This completes the preliminary processing.
The next step is to start decoding the soft-decision channel symbols. The decoder builds up a trellis of depth K x 5, and then traces back to the beginning of the trellis and outputs one bit. The decoder then shifts the trellis left one time instant, discarding the oldest data, following which it computes the accumulated error metrics for the next time instant, traces back, and outputs a bit. The decoder continues in this way until it reaches the flushing bits. The flushing bits cause the encoder to converge back to state 0, and the decoder exploits this fact. Once the decoder builds the trellis for the last bit, it flushes the trellis, decoding and outputting all the bits in the trellis up to but not including the first flushing bit.
I have compiled and tested the simulation source code described above under Borland C Builder Version 3-please do not request help in modifying the code to compile under a different environment. Simulation results are presented Click on one of the links below to go to the beginning of that section: Copyright 1999-2003, Spectrum Applications.
Coding is a technique where redundancy is added to original bit sequence to increase the reliability of the communication. In this article, lets discuss a simple binary convolutional coding scheme at the transmitter and the associated Viterbi (maximum likelihood) decoding scheme at the receiver.
Update: For some reason, the blog is unable to display the article which discuss both Convolutional coding and Viterbi decoding. As a work around, the article was broken upto into two posts. This post descrbes a simple Binary Convolutional Coding scheme. For details on the Viterbi decoding algorithm, please refer to the post – Chapter 8, Table 8.2-1 of lists the various rate 1/2 convolutional coding schemes.
The simplest among them has constraint length with generator polynomial. There are three parameters which define the convolotional code: (a) Rate: Ratio of the number of input bits to the number of output bits. In this example, rate is 1/2 which means there are two output bits for each input bit. (b) Constraint length: The number of delay elements in the convolutional coding. In this example, with there are two delay elements. (c) Generator polynomial: Wiring of the input sequence with the delay elements to form the output. In this example, generator polynomial is.
The output from the arm uses the XOR of the current input, previous input and the previous to previous input. The output from the uses the XOR of the current input and the previous to previous input. Figure 1: Convolutional code with Rate 1/2, K=3, Generator Polynomial 7,5 octal From the Figure 1, it can be seen that the operation on each arm is like a FIR filtering (aka convolution) with modulo-2 sum at the end (instead of a normal sum). Hence the name Convolutional code. State transition For understanding the Viterbi way of decoding the convolutional coded sequence, lets understand the relation between the input and output bits and the state transition. If ip = 0 if ip = 1 current state next state (op) next state (op) 00 00 (00) 10 (11) 01 00 (11) 10 (00) 10 01 (10) 11 (01) 11 01 (01) 11 (10) Table 1: State transition table and the output values.
Hi Dr.Krishna I am trying to implement you paper “A novel Arq technique using the turbo coding principle” I got the turbo decoder working, but in your paper you mention: when a retransmission takes place the LLR’s are used as a priori information. Before the LLR’s of the previous iteration are used in the current iteration what changes are to be done to the previous LLR;s. I am doing this: deinterleave to get original sequence and then interleave according to the interleaver pattern of second turbo enocder. Is there anything wrong in what i am doing to the LLR’s. Thank you, Arun.