Book ChapterDOI
An algebraic description of iterative decoding schemes
E. Offer,Emina Soljanin +1 more
- Vol. 123, pp 283-298
TLDR
It is explained exactly how suboptimal algorithms approximate the optimal, and it is shown how good these approximations are in some special cases.Abstract:
Several popular, suboptimal algorithms for bit decoding of binary block codes such as turbo decoding, threshold decoding, and message passing for LDPC, were developed almost as a common sense approach to decoding of some specially designed codes After their introduction, these algorithms have been studied by mathematical tools pertinent more to computer science than the conventional algebraic coding theory We give an algebraic description of the optimal and suboptimal bit decoders and of the optimal and suboptimal message passing We explain exactly how suboptimal algorithms approximate the optimal, and show how good these approximations are in some special casesread more
Citations
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Book
Information Theory, Inference and Learning Algorithms
TL;DR: A fun and exciting textbook on the mathematics underpinning the most dynamic areas of modern science and engineering.
Journal ArticleDOI
Constructing free-energy approximations and generalized belief propagation algorithms
TL;DR: This work explains how to obtain region-based free energy approximations that improve the Bethe approximation, and corresponding generalized belief propagation (GBP) algorithms, and describes empirical results showing that GBP can significantly outperform BP.
Journal ArticleDOI
Decoding of High Rate Convolutional Codes Using the Dual Trellis
S. Srinivasan,S.S. Pietrobon +1 more
TL;DR: This paper deals with a posteriori probability (APP) decoding of high-rate convolutional codes, using the dual code's trellis, and efficient techniques for normalization and extrinsic log-likelihood ratio (LLR) calculation are presented which reduce implementation complexity significantly.
Journal ArticleDOI
LDPC codes: a group algebra formulation
Emina Soljanin,Elke Offer +1 more
TL;DR: An entirely new approach to iterative decoding of low-density parity-check codes is proposed, which gives new insights into the issues of iterative decode from the algebraic coding theorist's point of view.
Journal ArticleDOI
Bit-optimal decoding of codes whose Tanner graphs are trees
E. Soljanin,E. Offer +1 more
TL;DR: A group algebra formulation for bit-optimal decoding of binary block codes is introduced to give a simple algebraic proof that Pearl's and Gallager's belief propagation decoding algorithms are bit-Optimal when the Tanner graph of the code is a tree.
References
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Book
Low-Density Parity-Check Codes
TL;DR: A simple but nonoptimum decoding scheme operating directly from the channel a posteriori probabilities is described and the probability of error using this decoder on a binary symmetric channel is shown to decrease at least exponentially with a root of the block length.
Proceedings ArticleDOI
Near Shannon limit error-correcting coding and decoding: Turbo-codes. 1
TL;DR: In this article, a new class of convolutional codes called turbo-codes, whose performances in terms of bit error rate (BER) are close to the Shannon limit, is discussed.
Journal ArticleDOI
Iterative decoding of binary block and convolutional codes
TL;DR: Using log-likelihood algebra, it is shown that any decoder can be used which accepts soft inputs-including a priori values-and delivers soft outputs that can be split into three terms: the soft channel and aPriori inputs, and the extrinsic value.
Near Shannon limit error-correcting coding and decoding
TL;DR: A new class of convolutional codes called turbo-codes, whose performances in terms of bit error rate (BER) are close to the Shannon limit, is discussed.