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Low-density parity-check codes with rates very close to the capacity of the q-ary symmetric channel for large q

Publications associées (155)

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Symmetric LDPC codes are not necessarily locally testable

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Locally testable codes, i.e., codes where membership in the code is testable with a constant number of queries, have played a central role in complexity theory. It is well known that a code must be a "low-density parity check" (LDPC) code for it to be loca ...

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The two central topics of information theory are the compression and the transmission of data. Shannon, in his seminal work, formalized both these problems and determined their fundamental limits. Since then the main goal of coding theory has been to find ...

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The invention of Fountain codes is a major advance in the field of error correcting codes. The goal of this work is to study and develop algorithms for source and channel coding using a family of Fountain codes known as Raptor codes. From an asymptotic poi ...

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Low-Density Codes Based on Chaotic Systems for Low-Density Codes Based on Chaotic Systems for Simple Encoding

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This paper proposes a new class of low-density generator-matrix codes (LDGM) based on chaotic dynamical systems. The codes are designed by controlling symbolic dynamics and using linear convolutional codes. Analyzing the complex structure of chaotic system ...

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Sharp Bounds for Optimal Decoding of Low Density Parity Check Codes

Nicolas Macris, Shrinivas Kudekar

Consider communication over a binary-input memoryless output-symmetric channel with low density parity check (LDPC) codes and maximum a posteriori (MAP) decoding. The replica method of spin glass theory allows to conjecture an analytic formula for the aver ...

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