Reed–Muller (RM) codes are known for their good maximum likelihood (ML) performance in
the short block-length regime. Despite being one of the oldest classes of channel codes …

Reed-Muller (RM) codes are among the oldest, simplest and perhaps most ubiquitous family
of codes. They are used in many areas of coding theory in both electrical engineering and …

Landmark codes underpin reliable physical layer communication, eg, Reed-Muller, BCH,
Convolution, Turbo, LDPC, and Polar codes: each is a linear code and represents a …

We propose a new class of efficient decoding algorithms for Reed-Muller (RM) codes over
binary-input memoryless channels. The algorithms are based on projecting the code on its …

In 1948, Shannon used a probabilistic argument to show that there exist codes achieving a
maximal rate defined by the channel capacity. In 1954, Muller and Reed introduced a simple …

The action of a noise operator on a code transforms it into a distribution on the respective
space. Some common examples from information theory include Bernoulli noise acting on a …

Abstract In 1984, Goldreich, Goldwasser and Micali formalized the concept of
pseudorandom functions and proposed a construction based on any length-doubling …

Reed-Muller (RM) codes are among the oldest, simplest and perhaps most ubiquitous family
of codes. They are used in many areas of coding theory in both electrical engineering and …

This work identifies information-theoretic quantities that are closely related to the required
list size on average for successive cancellation list (SCL) decoding to implement maximum …

While in the past several decades the trend to go towards increasing error-correcting code
lengths was predominant to get closer to the Shannon limit, applications that require short …