Signal Processing
Describes typical coding schemes like convolutional encoder, viterbi decoder, Hamming code etc
An earlier post we discussed hard decision decoding for a Hamming (7,4) code and simulated the the bit error rate. In this post, let us focus on the soft decision decoding for the Hamming (7,4) code, and quantify the bounds in the performance gain.
Continue reading “Hamming (7,4) code with soft and hard decoding”
In previous posts, we have discussed convolutional codes with Viterbi decoding (hard decision, soft decision and with finite traceback). Let us know discuss a block coding scheme where a group of information bits is mapped into
coded bits. Such codes are referred to as
codes. We will restrict the discussion to Hamming
codes, where 4 information bits are mapped into 7 coded bits. The performance with and without coding is compared using BPSK modulation in AWGN only scenario.
Continue reading “Hamming (7,4) code with hard decision decoding”
Are you bothered by speed of the speed of the simulations which you develop in Matlab/Octave? I was not bothered much, till I ran into the Viterbi decoder. If you recall, the Matlab/Octave simulation script for BER computation with hard soft decision Viterbi algorithm provided in post Viterbi with finite survivor state memory took around 10 hours to run.
In the post on Viterbi decoder and soft input Viterbi decoder, we discussed a convolutional encoding scheme with rate 1/2, constraint length and having generator polynomial
and having generator polynomial
. If the number of uncoded bits is
, then the number of coded bits at the output of the convolutional encoder is
. Decoding the convolutionaly encoded bits by Viterbi algorithm consisted of the following steps.
Continue reading “Viterbi with finite survivor state memory”
In two previous posts, we have discussed Convolutional Coding and the associated hard decision Viterbi decoding. In this post lets extent Viterbi decoding algorithm to soft input decision scheme. The modulation used is BPSK and the channel is assumed to be AWGN alone.
Coding is a technique where redundancy is added to original bit sequence to increase the reliability of the communication. 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 the Viterbi decoding algorithm for a simple Binary Convolutional Code with rate 1/2, constraint length and having generator polynomial
. For more details on the Binary convolutional code, please refer to the post – Convolutional code
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 – Viterbi decoder.
Chapter 8, Table 8.2-1 of Digital Communications by John Proakis 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:
