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In this paper, we consider low-complexity decoding of second-order Reed-Muller codes. A class of polynomial-time algorithms, based on the projections onto first-order codes, is studied. An old representative of this class, originally developed for binary s ...
In his landmark paper "A Mathematical Theory of Communication," the founding father of information theory and coding theory, Claude E. Shannon, established the largest rate at which reliable communication is possible and he revealed that the key to this re ...
Consider a binary linear code of length N, minimum distance d(min), transmission over the binary erasure channel with parameter 0 < epsilon < 1 or the binary symmetric channel with parameter 0 < epsilon < 1/2, and block-MAP decoding. It was shown by Tillic ...
Shannon, in his landmark 1948 paper, developed a framework for characterizing the fundamental limits of information transmission. Among other results, he showed that reliable communication over a channel is possible at any rate below its capacity. In 2008, ...
We are living in the era of "Big Data", an era characterized by a voluminous amount of available data. Such amount is mainly due to the continuing advances in the computational capabilities for capturing, storing, transmitting and processing data. However, ...
The concepts of pseudocodeword and pseudoweight play a fundamental role in the finite-length analysis of LDPC codes. The pseudoredundancy of a binary linear code is defined as the minimum number of rows in a parity-check matrix such that the corresponding ...
Reed-Muller (RM) codes were introduced in 1954 and have long been conjectured to achieve Shannon's capacity on symmetric channels. The activity on this conjecture has recently been revived with the emergence of polar codes. RM codes and polar codes are gen ...
The main objective of this paper is to explore the precise relationship between the Bethe free energy (or entropy) and the Shannon conditional entropy of graphical error correcting codes. The main result shows that the Bethe free energy associated with a l ...
In this paper, we consider the problem of decoding Reed-Muller (RM) codes in binary erasure channel. We propose a novel algorithm, which exploits several techniques, such as list recursive (successive cancellation) decoding based on Plotkin decomposition, ...
We present a coding paradigm that provides a new achievable rate for the primitive relay channel by combining compress-and-forward and decode-and-forward with a chaining construction. In the primitive relay channel model, the source broadcasts a message to ...
