EC-23.4 Modern Codes: Turbo, Low-Density Parity-Check and Polar
You can explain what iterative decoding does and why exchanging soft information between two decoders approaches the capacity limit, describe a low-density code by its graph, and say where each of the three families is used in current standards.
Before:S5-3. Digital Signal ProcessingEC-11. Data Communications and Computer Networks
For forty years the gap between what theory promised and what codes delivered stayed at several decibels. Three families closed it, and all three are now in standards a learner will meet. What they share is that decoding is iterative and approximate rather than exact, and that the structure is described by a graph. This topic is about the idea rather than the derivations, because the idea is what transfers.
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Iterative decoding, and passing soft information between two decoders
Two decoders each working on a differently interleaved version of the same data can hand each other their confidences and improve on each pass. Nothing about that guarantees convergence, and in practice it converges remarkably well.
NPTEL: Information Theory, Coding and Cryptography (IIT Delhi) · CourseThe turbo construction: two simple codes and an interleaver
Concatenating two ordinary convolutional codes through a long interleaver produces something enormously stronger than either. The interleaver is what makes the two decoders' errors independent enough for the exchange to help.
NPTEL: Error Control Coding — An Introduction to Convolutional Codes (IIT Kanpur) · CourseLow-density parity-check codes as a graph, and belief propagation on it
A sparse parity check matrix is drawn as a graph connecting bits to checks, and decoding passes probabilities along its edges. The sparsity is what keeps the message passing cheap enough to be worth doing.
NPTEL: Information Theory, Coding and Cryptography (IIT Delhi) · CoursePolar codes, and the idea of making channels reliable or useless on purpose
A transformation turns a set of identical channels into a set where some are almost perfect and the rest almost worthless, and information is sent only on the good ones. It is the first construction proved to reach capacity.
The error floor, and why a code that is excellent can still be unusable
Iterative decoders often improve rapidly and then flatten at an error rate far above zero, which matters enormously in storage and not at all in voice. Knowing whether an application cares is part of choosing a code.
Where each family is used, and what drove the choice
Standards bodies choose on decoding complexity, latency and flexibility of rate as much as on raw performance. Reading a standard's choice in that light explains decisions that look arbitrary otherwise.
NPTEL: Principles of Modern CDMA, MIMO and OFDM Wireless Communications (IIT Kanpur) · Course
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- FreeNPTEL / IIT Delhi · CourseNPTEL: Information Theory, Coding and Cryptography (IIT Delhi)
- FreeNPTEL / IIT Kanpur · CourseNPTEL: Error Control Coding — An Introduction to Convolutional Codes (IIT Kanpur)
- FreeNPTEL / IIT Kanpur · CourseNPTEL: Principles of Modern CDMA, MIMO and OFDM Wireless Communications (IIT Kanpur)
Links last checked 4 Sept 2026.
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