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We design sequences of low-density parity check codes that provably perform at rates extremely close to the Shannon capacity. These codes are built from highly irregular bipartite graphs with carefully chosen degree patterns on both sides. We further show ...
This paper starts a systematic study of capacity-achieving (c.a.) sequences of low-density parity-check codes for the erasure channel. We introduce a class A of analytic functions and develop a procedure to obtain degree distributions for the codes. We sho ...
The theory and practice of digital communication during the past 50 years has been strongly influenced by Shannon's separation theorem. While it is conceptually and practically appealing to separate source from channel coding, either step requires infinite ...
We analyze iterative coding for the frame-synchronous binary-input discrete-time Gaussian multiple access channel. Using the method of Density Evolution, we optimize degree distributions to exhibit code ensembles whose iterative decoding thresholds are onl ...
In this paper we will survey some of the most recent results on low-density parity-check codes. Our emphasis will be primarily on the asymptotic theory of these codes. For the most part, we will introduce the main concepts for the easier case of the erasur ...
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 ...
The complexity of channel equalization using the BCJR algorithn [1] grows exponentially with the channel memory. The M-BCJR algorithm [2], provides a method for reduced-trellis channel equalization. This paper examines the algorithm performance for differe ...
A method of encoding a message including a plurality of data items, includes identifying maximum and minimum numbers of first edges to be associated with data items. A first distribution of different numbers of first edges, ranging from the maximum to the ...
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 ...
Algebraic coding theory is one of the areas that routinely gives rise to computational problems involving various structured matrices, such as Hankel, Vandermonde, Cauchy matrices, and certain generalizations thereof. Their structure has often been used to ...
