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Iterative Quantization Using Codes On Graphs
TL;DR: The results suggest that graphical models may yield near optimal codes in source coding as well as in channel coding and that duality plays a key role in such constructions.
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Abstract: We study codes on graphs combined with an iterative message passing algorithm for quantization. Specifically, we consider the binary erasure quantization (BEQ) problem which is the dual of the binary erasure channel (BEC) coding problem. We show that duals of capacity achieving codes for the BEC yield codes which approach the minimum possible rate for the BEQ. In contrast, low density parity check codes cannot achieve the minimum rate unless their density grows at least logarithmically with block length. Furthermore, we show that duals of efficient iterative decoding algorithms for the BEC yield efficient encoding algorithms for the BEQ. Hence our results suggest that graphical models may yield near optimal codes in source coding as well as in channel coding and that duality plays a key role in such constructions.
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Citations
Performance of polar codes for channel and source coding
Nadine Hussami,Satish Babu Korada,Rudiger Urbanke +2 more
- 28 Jun 2009
TL;DR: The polar codes, introduced by Arikan, are the first family of codes known to achieve capacity of symmetric channels using a low-complexity successive cancellation decoder as discussed by the authors.
370
Polar Codes for Channel and Source Coding
Satish Babu Korada
- 19 Jan 2009
TL;DR: This thesis constructs polar codes that asymptotically approach Shannon's rate-distortion bound for a large class of sources and proposes algorithms based on message-passing to improve the finite length performance of polar codes.
364
Polar Codes are Optimal for Lossy Source Coding
TL;DR: The optimality of polar codes for various multiterminal problems including the binary Wyner-Ziv and the binary Gelfand-Pinsker problems is shown and the results extend to general versions of these problems.
363
Fixed-Length Lossy Compression in the Finite Blocklength Regime
Victoria Kostina,Sergio Verdu +1 more
TL;DR: For stationary memoryless sources with separable distortion, the minimum rate achievable is shown to be closely approximated by the standard Gaussian complementary cumulative distribution function.
Fixed-length lossy compression in the finite blocklength regime
Victoria Kostina,Sergio Verdu +1 more
TL;DR: In this paper, the authors studied the minimum achievable source coding rate as a function of blocklength and probability that the distortion exceeds a given level, and derived tight general achievability and converse bounds that hold at arbitrary fixed blocklength.
References
Quantization
Robert M. Gray,David L. Neuhoff +1 more
TL;DR: The key to a successful quantization is the selection of an error criterion – such as entropy and signal-to-noise ratio – and the development of optimal quantizers for this criterion.
2.1K
Codes on graphs: normal realizations
G.D. Forney
- 25 Jun 2000
TL;DR: Any state realization of a code can be put into normal form without essential change in the corresponding graph or in its decoding complexity; this fundamental result has many applications, including to dual state spaces, dual minimal trellises, duals to Tanner (1981) graphs, dual input/output (I/O) systems, and dual kernel and image representations.
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•Posted Content
Constraint Satisfaction by Survey Propagation
TL;DR: In this article, a generic formalism for survey propagation for a wide class of discrete constraint satisfiability problems is presented. But this formalism is not applicable to the survey propagation problem.
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Constraint Satisfaction by Survey Propagation
Alfredo Braunstein,Marc Mézard,Martin Weigt,Riccardo Zecchina +3 more
- 01 Jan 2006
TL;DR: Here a generic formalism is provided which applies to a wide class of discrete Constraint Satisfaction Problems and is successfully tested on random 3-SAT and random graph 3-coloring.
Capacity-achieving sequences for the erasure channel
P. Oswald,Amin Shokrollahi +1 more
- 24 Jun 2001
TL;DR: It turns out that the right-regular sequence is c.a. in a much stronger sense than, e.g., the Tornado sequence, which explains why numerical optimization techniques tend to favor graphs with only one degree of check nodes.
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