Channel Coding Archives - GaussianWaves

Convolutional Codes – sliding window and shift register

Mathuranathan — Fri, 25 Aug 2023 13:00:00 +0000

Key focus : Convolutional codes: Error-correcting codes effective in noisy channels and burst error correction. Know about sliding window & shift registers and how they are used in a convolutional encoder. Linear block codes Linear block codes, like Hamming codes, are mainly employed in hard decision decoding, utilizing the inherent algebraic structure of the code ... Read more

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Euclidean and Hamming distances

Mathuranathan — Wed, 23 Sep 2020 08:34:48 +0000

Key focus: Euclidean & Hamming distances are used to measure similarity or dissimilarity between two sequences. Used in Soft & Hard decision decoding. Distance is a measure that indicates either similarity or dissimilarity between two words. Given a pair of words a=(a0,a1, … ,an-1) and b=(b0,b1,…,bn-1) , there are variety of ways one can characterize ... Read more

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Hidden Markov Models (HMM) – Simplified !!!

Mathuranathan — Tue, 17 Mar 2020 05:08:35 +0000

Markov chains are useful in computing the probability of events that are observable. However, in many real world applications, the events that we are interested in are usually hidden, that is we don’t observe them directly. These hidden events need to be inferred. For example, given a sentence in a natural language we only observe the ... Read more

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Markov Chains – Simplified !!

Mathuranathan — Fri, 06 Mar 2020 07:11:37 +0000

Key focus: Markov chains are a probabilistic models that describe a sequence of observations whose occurrence are statistically dependent only on the previous ones. ● Time-series data like speech, stock price movements.● Words in a sentence.● Base pairs on the rung of a DNA ladder. States and transitions Assume that we want to model the ... Read more

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Shannon limit on power efficiency – demystified

Mathuranathan — Wed, 20 Nov 2019 10:07:31 +0000

The Shannon power efficiency limit is the limit of a band-limited system irrespective of modulation or coding scheme. It informs us the minimum required energy per bit required at the transmitter for reliable communication. It is also called unconstrained Shannon power efficiency Limit. If we select a particular modulation scheme or an encoding scheme, we ... Read more

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Block Interleaver Design for RS codes

Mathuranathan — Thu, 28 Oct 2010 08:18:00 +0000

Introduction: A Reed Solomon (RS) encoder, takes user data symbols and converts it into a n symbol wide codeword, by adding parity symbols. The error correcting capability of the RS code is computed as . That is, a RS code with parity symbols can correct a burst error of upto symbol errors. Block Interleavers: Suppose, ... Read more

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Viterbi Decoding of Convolutional codes

Mathuranathan — Thu, 17 Jun 2010 03:58:00 +0000

Viterbi algorithm is utilized to decode the convolutional codes. Again the decoding can be done in two approaches. One approach is called hard decision decoding which uses Hamming distance as a metric to perform the decoding operation, whereas, the soft decision decoding uses Euclidean distance as a metric. As stated in one of the previous ... Read more

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Maximum Likelihood estimation

Mathuranathan — Thu, 07 Jan 2010 02:52:00 +0000

Keywords: maximum likelihood estimation, statistical method, probability distribution, MLE, models, practical applications, finance, economics, natural sciences. Introduction Maximum Likelihood Estimation (MLE) is a statistical method used to estimate the parameters of a probability distribution by finding the set of values that maximize the likelihood function of the observed data. In other words, MLE is a ... Read more

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Maximum Likelihood Decoding

Mathuranathan — Wed, 06 Jan 2010 10:09:00 +0000

Keywords: maximum likelihood decoding, digital communication, data storage, noise, interference, wireless communication systems, optical communication systems, digital storage systems, probability, likelihood estimation, python Introduction Maximum likelihood decoding is a technique used to determine the most likely transmitted message in a digital communication system, based on the received signal and statistical models of noise and interference. ... Read more

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Hard and Soft decision decoding

Mathuranathan — Tue, 29 Dec 2009 06:40:00 +0000

What are hard and soft decision decoding Hard decision decoding and soft decision decoding are two different methods used for decoding error-correcting codes. With hard decision decoding, the received signal is compared to a set threshold value to determine whether the transmitted bit is a 0 or a 1. This is commonly used in digital ... Read more

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