We introduce a new approach to proving that a sequence of deterministic linear codes
achieves capacity on an erasure channel under maximum a posteriori decoding. Rather …

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 …

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 …

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 …

This paper studies the parameters for which binary Reed-Muller (RM) codes can be
decoded successfully on the BEC and BSC, and in particular when can they achieve …

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 proves new results on the ability of binary Reed-Muller codes to decode from
random errors and erasures. Specifically, we prove that RM codes with m variables and …

We present the first local list-decoding algorithm for the rth order Reed-Muller code RM (2,
m) over F for r≥ 2. Given an oracle for a received word R: Fm-< F, our randomized local list …

We strengthen the results from a recent work by the second author, achieving bounds on the
weight distribution of binary linear codes that are successful under block-MAP (as well as bit …

Pre-transformation with an upper-triangular matrix (including cyclic redundancy check
(CRC), parity-check (PC) and polarization-adjusted convolutional (PAC) codes) improves …