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Asymptotic and finite-length analysis of low-density parity-check codes

Publications associées (268)

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Improved low-density parity-check codes using irregular graphs

Mohammad Amin Shokrollahi

We construct new families of error-correcting codes based on Gallager's (1973) low-density parity-check codes. We improve on Gallager's results by introducing irregular parity-check matrices and a new rigorous analysis of hard-decision decoding of these co ...

2001

Efficient erasure correcting codes

Mohammad Amin Shokrollahi

We introduce a simple erasure recovery algorithm for codes derived from cascades of sparse bipartite graphs and analyze the algorithm by analyzing a corresponding discrete-time random process. As a result, we obtain a simple criterion involving the fractio ...

Institute of Electrical and Electronics Engineers2001

To Code, Or Not To Code: On the Optimality of Symbol-by-Symbol Communication

Martin Vetterli, Michael Christoph Gastpar, Bixio Rimoldi

When is uncoded transmission optimal? This paper derives easy-to-check necessary and sufficient conditions that do not require finding the rate-distortion and the capacity-cost functions. We consider the symbol-by-symbol communication of discrete-time memo ...

2001

Turbo Encoder Design for Symbol Interleaved Parallel Concatenated Trellis Coded Modulation

Christina Fragouli

This paper addresses turbo-encoder design for coding with high spectral efficiency using parallel concatenated trellis-coded modulation and symbol interleaving. The turbo-encoder design involves the constituent encoder design and the interleaver design. Th ...

2001

Turbo Codes with Non-Uniform Constellation

Christina Fragouli

This paper presents parallel concatenated turbo codes that employ a non-uniform constellation to achieve shaping gain. The output signal approximates the Gaussian distribution by using equally likely signals with unequal spacing (a non-uniform constellatio ...

2001

Bit vs. Symbol Interleaving for Parallel Concatenated Trellis Coded Modulation

Christina Fragouli

This paper compares bit versus symbol interleaving for parallel-concatenated trellis-coded turbo codes, employing the turbo encoder structure proposed in Benedetto et al., (1996). To compare systems optimized with the same techniques, the paper extends the ...

2001

Minimality for puncturing convolutional codes

Christina Fragouli

This paper investigates encoders optimization for the Hamming weight after periodic puncturing, and discusses minimality issues that may affect the performance of the punctured encoders. Periodically puncturing a minimal encoder produces a higher rate enco ...

2001

On source/channel codes of finite block length

Martin Vetterli, Michael Christoph Gastpar, Bixio Rimoldi

For certain fortunate choices of source/channel pairs, all sophisticated coding is in vain: for them, a code of block length one is sufficient to achieve optimal performance \cite{mgbrmvtrans}. Is the set of ``fortunate choices'' larger if we allow for cod ...

2001

Codes and Graphs

Mohammad Amin Shokrollahi

In this paper, I will give a brief introduction to the theory of low-density parity- check codes, and their decoding. I will emphasize the case of correcting erasures as it is still the best understood and most accessible case. At the end of the paper, I w ...

Springer2000

Using low density parity check codes in the McEliece cryptosystem

Mohammad Amin Shokrollahi, Joachim Rosenthal

We examine the implications of using a low density parity check code (LDPCC) in place of the usual Goppa code in McEliece's cryptosystem. Using a LDPCC allows for larger block lengths and the possibility of a combined error correction/encryption protocol ...

2000