| Information Theory and Coding |
| Subtitle: |
| This course is part of the module: Information Theory and Coding |
| Semester: |
| SoSe 24 |
| Course type: |
| Lecture |
| Course number: |
| lv436_s24 |
| Lecturer: |
| Gerhard Bauch, Philipp Mohr, PD Dr.-Ing. habil. Rainer Grünheid |
| Description: |
- Introductionto information theory and coding
- Definitionsof information: Self information, entropy
- Binaryentropy function
- Sourcecoding theorem
- Entropyof continuous random variables: Differential entropy, differential entropy ofuniformly and Gaussian distributed random variables
- Sourcecoding
- Principlesof lossless source coding
- Optimalsource codes
- Prefixcodes, prefix-free codes, instantaneous codes
- Morsecode
- Huffmancode
- Shannoncode
- Boundson the average codeword length
- Relativeentropy, Kullback-Leibler distance, Kullback-Leibler divergence
- Crossentropy
- Lempel-Zivalgorithm
- Lempel-Ziv-Welch(LZW) algorithm
- Textcompression and image compression using variants of the Lempel-Ziv algorithm
- Channelmodels
- AWGNchannel
- Binary-inputAWGN channel
- Binarysymmetric channel (BSC)
- Relationshipbetween AWGN channel and BSC
- Binaryerror and erasure channel (BEEC)
- Binaryerasure channel (BEC)
- Discretememoryless channels (DMC)
- Definitionsof information for multiple random variables
- Mutualinformation and channel capacity
- Entropy,conditional entropy
- Chainrules for entropy and mutual information
- Channelcoding theorem
- Channelcapacity of fundamental channels: BSC, BEC, AWGN channel, binary-input AWGNchannel etc.
- Power-limitedvs. bandlimited transmission
- Capacityof parallel AWGN channels
- Waterfilling
- Examples:Multiple input multiple output (MIMO) channels, complex equivalent basebandchannels, orthogonal frequency division multiplex (OFDM)
- Source-channelcoding theorem, separation theorem
- Multiuserinformation theory
- Multipleaccess channel (MAC)
- Broadcastchannel
- Principlesof multiple access, time division multiple access (TDMA), frequency divisionmultiple access (FDMA), non-orthogonal multiple access (NOMA), hybrid multipleaccess
- Achievablerate regions of TDMA and FDMA with power constraint, energy constraint, powerspectral density constraint, respectively
- Achievablerate region of the two-user and K-user multiple access channels
- Achievablerate region of the two-user and K user broadcast channels
- Multiuserdiversity
- Channelcoding
- Principlesand types of channel coding
- Coderate, data rate, Hamming distance, minimum Hamming distance, Hamming weight,minimum Hamming weight
- Errordetecting and error correcting codes
- Simpleblock codes: Repetition codes, single parity check codes, Hamming code, etc.
- Syndromedecoding
- Representationsof binary data
- Non-binarysymbol alphabets and non-binary codes
- Codeand encoder, systematic and non-systematic encoders
- Propertiesof Hamming distance and Hamming weight
- Decodingspheres
- Perfectcodes
- Linearcodes
- Decodingprinciples
- Syndromedecoding
- Maximuma posteriori probability (MAP) decoding and maximum likelihood (ML) decoding
- Harddecision and soft decision decoding
- Log-likelihoodratios (LLRs), boxplus operation
- MAPand ML decoding using log-likelihood ratios
- Soft-insoft-out decoders
- Errorrate performance comparison of codes in terms of SNR per info bit vs. SNR percode bit
- Linearblock codes
- Generatormatrix and parity check matrix, properties of generator matrix and parity checkmatrix
- Dualcodes
- Lowdensity parity check (LDPC) codes
- Sparseparity check matrix
- Tannergraphs, cycles and girth
- Degreedistributions
- Coderate and degree distribution
- Regularand irregular LDPC codes
- Messagepassing decoding
- Messagepassing decoding in binary erasure channels (BEC)
- Systematicencoding using erasure message passing decoding
- Messagepassing decoding in binary symmetric channels (BSC)
- Extrinsicinformation
- Bit-flippingdecoding
- Effectsof short cycles in the Tanner graph
- Alternativebit-flipping decoding
- Softdecision message passing decoding: Sum product decoding
- Biterror rate performance of LDPC codes
- Repeataccumulate codes and variants of repeat accumulate codes
- Messagepassing decoding and turbo decoding of repeat accumulate codes
- Convolutionalcodes
- Encodingusing shift registers
- Trellisrepresentation
- Harddecision and soft decision Viterbi decoding
- Biterror rate performance of convolutional codes
- Asymptoticcoding gain
- Viterbidecoding complexity
- Freedistance and optimum convolutional codes
- Generatorpolynomial description and octal description
- Catastrophicconvolutional codes
- Non-systematicand recursive systematic convolutional (RSC) encoders
- Ratecompatible punctured convolutional (RCPC) codes
- Hybridautomatic repeat request (HARQ) with incremental redundancy
- Unequalerror protection with punctured convolutional codes
- Errorpatterns of convolutional codes
- Concatenatedcodes
- Serialconcatenated codes
- Parallelconcatenated codes, Turbo codes
- Iterativedecoding, turbo decoding
- Biterror rate performance of turbo codes
- Interleaverdesign for turbo codes
- Codedmodulation
- Principleof coded modulation
- Achievablerates with PSK/QAM modulation
- Trelliscoded modulation (TCM)
- Setpartitioning
- Ungerböckcodes
- Multilevelcoding
- Bit-interleavedcoded modulation
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| Performance accreditation: |
| 605 - Information Theory and Coding<ul><li>605 - Information Theory and Coding: Klausur schriftlich</li></ul> |
| ECTS credit points: |
| 4 |
| Stud.IP informationen about this course: |
Home institute: Institut für Nachrichtentechnik (E-8)
Registered participants in Stud.IP: 138
Postings: 7
Documents: 34
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