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Lecture

Convolutional Codes & Viterbi Decoder

In course

EE-543: Advanced wireless receivers

Students extend their knowledge on wireless communication systems to spread-spectrum communication and to multi-antenna systems. They also learn about the basic information theoretic concepts, about channel coding, and bit-interleaved coded modulation. ...

Description

This lecture covers Convolutional Codes, which transform information sequences into coded symbols with memory, and the Viterbi Algorithm for low-complexity decoding. It explains the state diagram and trellis diagram representations, the branch metric computation, and the state metric updates. The Viterbi Algorithm is detailed, including branch and state metric computations, and the traceback process. The lecture also discusses the high-level architecture of the Viterbi Algorithm, state metric computation using Add Compare Select (ACS), and examples of forward and backward iterations. It concludes with insights on limiting the survivor path length in large code blocks.

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Ontological neighbourhood

Information engineering

Information theory: Coding theory

Related concepts (32)

Convolutional code

In telecommunication, a convolutional code is a type of error-correcting code that generates parity symbols via the sliding application of a boolean polynomial function to a data stream. The sliding application represents the 'convolution' of the encoder over the data, which gives rise to the term 'convolutional coding'. The sliding nature of the convolutional codes facilitates trellis decoding using a time-invariant trellis. Time invariant trellis decoding allows convolutional codes to be maximum-likelihood soft-decision decoded with reasonable complexity.

Viterbi decoder

A Viterbi decoder uses the Viterbi algorithm for decoding a bitstream that has been encoded using a convolutional code or trellis code. There are other algorithms for decoding a convolutionally encoded stream (for example, the Fano algorithm). The Viterbi algorithm is the most resource-consuming, but it does the maximum likelihood decoding. It is most often used for decoding convolutional codes with constraint lengths k≤3, but values up to k=15 are used in practice. Viterbi decoding was developed by Andrew J.

Error correction code

In computing, telecommunication, information theory, and coding theory, forward error correction (FEC) or channel coding is a technique used for controlling errors in data transmission over unreliable or noisy communication channels. The central idea is that the sender encodes the message in a redundant way, most often by using an error correction code or error correcting code (ECC). The redundancy allows the receiver not only to detect errors that may occur anywhere in the message, but often to correct a limited number of errors.

Turbo code

In information theory, turbo codes (originally in French Turbocodes) are a class of high-performance forward error correction (FEC) codes developed around 1990–91, but first published in 1993. They were the first practical codes to closely approach the maximum channel capacity or Shannon limit, a theoretical maximum for the code rate at which reliable communication is still possible given a specific noise level. Turbo codes are used in 3G/4G mobile communications (e.g.

Coding theory

Coding theory is the study of the properties of codes and their respective fitness for specific applications. Codes are used for data compression, cryptography, error detection and correction, data transmission and data storage. Codes are studied by various scientific disciplines—such as information theory, electrical engineering, mathematics, linguistics, and computer science—for the purpose of designing efficient and reliable data transmission methods.

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Convolutional Codes: Encoding and Decoding

Explains the encoding and decoding process of convolutional codes using constellation prints.

Convolutional Codes: Basics and Applications

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