167 research outputs found
Decoding of Non-Binary LDPC Codes Using the Information Bottleneck Method
Recently, a novel lookup table based decoding method for binary low-density
parity-check codes has attracted considerable attention. In this approach,
mutual-information maximizing lookup tables replace the conventional operations
of the variable nodes and the check nodes in message passing decoding.
Moreover, the exchanged messages are represented by integers with very small
bit width. A machine learning framework termed the information bottleneck
method is used to design the corresponding lookup tables. In this paper, we
extend this decoding principle from binary to non-binary codes. This is not a
straightforward extension, but requires a more sophisticated lookup table
design to cope with the arithmetic in higher order Galois fields. Provided bit
error rate simulations show that our proposed scheme outperforms the log-max
decoding algorithm and operates close to sum-product decoding.Comment: This paper has been presented at IEEE International Conference on
Communications (ICC'19) in Shangha
Modern Coding Theory: The Statistical Mechanics and Computer Science Point of View
These are the notes for a set of lectures delivered by the two authors at the
Les Houches Summer School on `Complex Systems' in July 2006. They provide an
introduction to the basic concepts in modern (probabilistic) coding theory,
highlighting connections with statistical mechanics. We also stress common
concepts with other disciplines dealing with similar problems that can be
generically referred to as `large graphical models'.
While most of the lectures are devoted to the classical channel coding
problem over simple memoryless channels, we present a discussion of more
complex channel models. We conclude with an overview of the main open
challenges in the field.Comment: Lectures at Les Houches Summer School on `Complex Systems', July
2006, 44 pages, 25 ps figure
Soft-Decoding-Based Strategies for Relay and Interference Channels: Analysis and Achievable Rates Using LDPC Codes
We provide a rigorous mathematical analysis of two communication strategies:
soft decode-and-forward (soft-DF) for relay channels, and soft partial
interference-cancelation (soft-IC) for interference channels. Both strategies
involve soft estimation, which assists the decoding process. We consider LDPC
codes, not because of their practical benefits, but because of their analytic
tractability, which enables an asymptotic analysis similar to random coding
methods of information theory. Unlike some works on the closely-related
demodulate-and-forward, we assume non-memoryless, code-structure-aware
estimation. With soft-DF, we develop {\it simultaneous density evolution} to
bound the decoding error probability at the destination. This result applies to
erasure relay channels. In one variant of soft-DF, the relay applies Wyner-Ziv
coding to enhance its communication with the destination, borrowing from
compress-and-forward. To analyze soft-IC, we adapt existing techniques for
iterative multiuser detection, and focus on binary-input additive white
Gaussian noise (BIAWGN) interference channels. We prove that optimal
point-to-point codes are unsuitable for soft-IC, as well as for all strategies
that apply partial decoding to improve upon single-user detection (SUD) and
multiuser detection (MUD), including Han-Kobayashi (HK).Comment: Accepted to the IEEE Transactions on Information Theory. This is a
major revision of a paper originally submitted in August 201
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