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Coding Theory (Error Detection and Error Correction)

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Error Detection and Correction Techniques Error Detection and Correction Techniques Introduction Error detection and correction are essential in digital communications and storage systems to ensure data integrity. Errors can occur due to noise, interference, or hardware malfunctions. Basic Concepts Error Detection: Identifying whether errors have occurred in transmitted data Error Correction: Identifying and correcting errors in transmitted data Redundancy: Adding extra bits to detect or correct errors Forward Error Correction (FEC): Ability to correct errors without retransmission Common Techniques 1. Parity Check The simplest form of error detection that uses a single parity bit. Types: Even Parity: Parity bit makes total number of 1s even Odd Parity: Parity bit makes total number of 1s odd Even Par...
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Digital Signal Processing

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DSP for Wireless Domain - Interview Preparation (Enhanced) Digital Signal Processing (DSP) for Wireless Domain - Interview Preparation (Enhanced) This document summarizes key DSP concepts, including examples, mathematical equations, and text-based block diagrams, tailored for a DSP engineer position interview in the wireless domain. 1. Fundamentals of Signal Conversion (Analog to Digital) Wireless signals are inherently analog and continuous. DSP involves converting these to digital for processing. Sampling The process of converting a continuous-time signal \(x(t)\) into a discrete-time signal \(x[n]\) by taking its amplitude measurements at regular intervals, where \(x[n] = x(nT_s)\) and \(T_s\) is the sampling period. The sampling rate is \(F_s = 1/T_s\). Nyquist-Shannon Sampling Theorem: To perfectly reconstruct an analog...
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Channel Equalization

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Channel Equalization Tutorial Channel Equalization Tutorial 1. Introduction to Channel Impairments In digital communication systems, signals often travel through various physical media (e.g., copper wires, optical fibers, wireless channels). These channels are rarely ideal and introduce distortions that can severely degrade the quality of the received signal. These distortions are generally referred to as channel impairments . Key impairments include: Noise: Unwanted random fluctuations added to the signal (e.g., thermal noise, shot noise, interference). Inter-symbol Interference (ISI): This is a primary concern. ISI occurs when the spreading of a pulse for one symbol overlaps with subsequent symbols, causing a "smearing" effect and making it difficult to distinguish individual symbols. This is typically caused by multipath propagation or the frequency-selective natur...
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Channel Estimation

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Channel Estimation Tutorial Channel Estimation: A Comprehensive Tutorial 1. Introduction to Channel Estimation In wireless communication, signals travel through a complex environment before reaching the receiver. This environment, known as the **wireless channel**, can significantly alter the transmitted signal due to phenomena like reflection, diffraction, scattering, and absorption. These effects lead to issues such as signal attenuation, phase shifts, and multipath fading. To accurately decode the original information at the receiver, it is crucial to understand and compensate for these channel impairments. This process is known as **channel estimation**. What is the Wireless Channel? The wireless channel can be modeled as a linear system characterized by its **impulse response** or **frequency response**. For a simple single-input single-output (SISO) system, the received ...
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