Linear block code
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Linear block codes encode messages by adding parity bits to create codewords. They have the following properties: 1) They encode a k-bit message into an n-bit codeword, where n-k bits are parity bits calculated from the message bits. 2) Syndrome decoding uses the parity check matrix H to detect and locate errors by calculating the syndrome s, which depends only on the error pattern. 3) A linear block code can correct up to t errors per codeword if the minimum distance dmin is greater than 2t+1.
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The syndrome s is the sum of those columns of
matrix H corresponding to the error locations
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correct all error patterns of weight t or less if
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An (n,k) linear block code of minimum distance dmin
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More from Manish Srivastava (20)
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Vhf communication system for cross country pipelines Manish Srivastava This document discusses the implementation of a VHF radio trunking communication system for an oil pipeline running between Mundra and Delhi in India. It provides secure and independent communication between vehicles, handheld radios, and fixed locations along the pipeline. The system allows for different types of calls including private calls, group calls, and emergency calls. It ensures communication continuity as users move between different locations along the pipeline route. The benefits highlighted are 24/7 seamless communication for enhanced pipeline security without reliance on external cellular networks.
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Need for sulphur measurement in multi product pipelinesManish Srivastava The document discusses the need for rapid sulphur measurement in multi-product pipelines. It notes that different product batches are pushed through pipelines abutting each other, and accurate sulphur measurement is needed to minimize contamination between batches. The PAC Antek High Speed Sulphur Analyzer provides sulphur measurements in under 1 minute, much faster than other techniques, allowing for more precise interface detection between products to reduce contamination and transmix volumes. Field tests in India found the analyzer could save over $4,000 per product cut compared to slower analyzing techniques.
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Wcdma channels Manish Srivastava WCDMA uses an OSI model with 7 layers. The lower 3 layers - physical, data link, and network layers - are most important for WCDMA. The physical layer uses different physical channels to transmit data over the air interface. Logical channels define how data is transferred, transport channels define how data is transmitted, and physical channels carry payload data and define signal characteristics. There are three types of channels - logical, transport, and physical - that work together to transmit various types of control and traffic data between the UE and base station.
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Harq
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Impact of channel in wireless communication
Impact of channel in wireless communicationManish Srivastava Wireless telecommunications involves the transfer of information between two or more points without a physical connection. It uses forms of energy like radio frequencies to transmit information over various distances, from a few meters to thousands of kilometers. While wireless operations allow for long-range communication without wires, the wireless channel is susceptible to factors like interference, path loss, and fading that restrict reliability and throughput. Adaptation techniques and MIMO can help improve performance but spectrum and interference remain limitations of wireless networks.
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Hspa and hsdpaManish Srivastava HSPA is a mobile telecommunications protocol that extends 3G networks by improving data transmission rates. It consists of HSDPA for faster downloads and HSUPA for faster uploads. HSPA was designed for non-real time data and increases peak rates to 14Mbps down and 5.8Mbps up. It achieves these improvements through technologies like shorter transmission time intervals, link adaptation, advanced modulation schemes, and MIMO antennas. The architecture introduces new channels like HS-DSCH for user data and HS-SCCH for control information. Subsequent evolutions like HSPA+ and DC-HSDPA have further increased speeds through higher order modulation and dual-cell connections.
Harq
HarqManish Srivastava HARQ is a technique that combines error correction codes with automatic repeat requests (ARQ). It allows errors that are uncorrectable by the error correction code alone to be corrected through retransmissions. There are two main types of HARQ - Type I adds error detection and forward error correction to each message, while Type II alternates between message bits and error detecting parity bits. Soft combining at the receiver improves performance by combining incorrectly received blocks with retransmissions. Incremental redundancy, used in technologies like HSDPA, improves performance over chase combining by sending different coded bits with each retransmission. HARQ is used in mobile networks to provide high speed data transmission.
Handover
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Convolution codes and turbo codes
Convolution codes and turbo codesManish Srivastava Convolution codes and turbo codes are error-correcting codes used to reliably transmit digital data over noisy communication channels. Convolution codes work by convolving the sequence of information bits according to some rule, spreading the bits along the coded sequence. Turbo codes achieve better error correction than convolution codes through the parallel concatenation of convolutional encoders separated by an interleaver, along with iterative decoding. The Viterbi algorithm is typically used to decode convolution codes by finding the most probable state sequence, while turbo codes use two decoders and feedback to iteratively improve the decoding of each encoded sequence.
Control plane
Control planeManish Srivastava This document discusses the key interfaces, architecture, and procedures related to control and user planes, mobility management, and connection management in 3G networks. The control plane handles protocols for controlling radio access bearers and the connection between UE and network. It has physical, data link, and network layers. The user plane is responsible for transferring user data through access and core network protocols. Mobility management allows tracking and delivering services to mobile subscribers via location management, registration, and security functions. Connection management establishes and maintains connections to exchange information with peer entities.
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Comparison between 2g, 2.5g, 3g, lte and lte aManish Srivastava This document summarizes the evolution of mobile networks from 2G to 4G. It describes the key technologies and capabilities of 2G (9.6 Kbps speed), 2.5G/GPRS (up to 115 Kbps), 3G (2 Mbps, increased bandwidth to 2GHz, supports video/GPS), LTE (200 active clients per 5MHz cell, up to 2Gbps speed), and 4G (formally approved in 2009 as IMT-Advanced, 2Gbps speed, improved coverage and capacity). Each generation brought increased speeds and bandwidth as well as new multimedia capabilities.
Pigging In OIL INDUSTRY
Pigging In OIL INDUSTRY Manish Srivastava This document provides an overview of intelligent pigging and the intelligent pigging survey of a 14-inch crude oil pipeline from Barauni Pump Station to Pump Station 5 that is 756 km long. Intelligent pigging uses specially designed tools called "pigs" to inspect and clean pipelines without stopping flow. The document discusses the types of pigs used for different pipeline activities like construction, maintenance, and operation. It also summarizes the goals and activities of the survey conducted by Rosen Europe B.V. on the 14-inch pipeline, including using a corrosion detection pig (CDP) to detect metal loss and pipe wall defects.
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Linear block code
- 1. LINEAR BLOCK CODING Presented by: Manish Srivastava
- 2. LINEAR BLOCK CODE In a (n,k) linear block code: 1st portion of k bits is always identical to the message sequence to be transmitted. 2nd portion of (n-k ) bits are computed from message bits according to the encoding rule and is called parity bits.
- 3. SYNDROME DECODING The generator matrix G is used in the encoding operation at the transmitter The parity- check matrix H is used in the decoding operation at the receiver Let , y denote 1-by-n received vector that results from sending the code x over a noisy channel y=x +e
- 4. For i=1,2,….., n ei= 1,if an error has occurred in the ith location 0 ,otherwise o s=yHt
- 5. PROPERTIES Property 1: The syndrome depends only on the error pattern and not on the transmitted code word. S=(x+e)Ht =xHt+ eHt =eHt
- 6. PROPERTY 2: All error pattern that differs at most by a code word have the same syndrome. For k message bits ,there are 2k distinct codes denoted as xi ,i=0,1, ………. 2k -1 we define 2k distinct vectors as e =e+ xi i=0,1,…….. 2k-1
- 7. =e + =e
- 8. PROPERTY 3: The syndrome s is the sum of those columns of matrix H corresponding to the error locations H=[ , ………., ] therefore, s=
- 9. PROPERTY 4: With syndrome decoding ,an (n,k) linear block code can correct up to t errors per code word ,provided that n and k satisfy the hamming bound ≥ ( ) where ( ) is a binomial coefficient ,namely ( )= n!/(n-i)!i!
- 10. MINIMUM DISTANCE CONSIDERATIONS: Consider a pair of code vectors x and y that have the same number of elements Hamming distance d(x,y): It is defined as the number of locations in which their respective elements differ . Hamming weight w(x) : It is defined as the number of elements in the code vector.
- 11. Minimum distance dmin: It is defined as the smallest hamming distance between any pair of code vectors in the code or smallest hamming weight of the non zero code vectors in the code .
- 12. An (n,k) linear block code has the power to correct all error patterns of weight t or less if ,and only if d( ) ≤2t+1 An (n,k) linear block code of minimum distance dmin can correct upto 1 error if and only if t≤ [1/2 (dmin – 1)].
- 13. Advantages Disadvantages Easiest to detect and Transmission correct errors. bandwidth is more. Extra parity bit does not Extra bit reduces the convey any information bit rate of transmitter but detects and and also its power. corrects errors.
- 14. APPLICATIONS Used for error control coding. Storage-magnetic and optical data storage in hard disks and magnetic tapes and single error correcting and double error correcting code(SEC- DEC) used to improve semiconductor memories. Communication-satellite and deep space communications.
- 15. THANK YOU!!