Related papers: Reed-Muller codes have vanishing bit-error probabi…
Data transmission from superconducting digital electronics such as single flux quantum (SFQ) logic to semiconductor (CMOS) circuits is subject to bit errors due to, e.g., flux trapping, process parameter variations (PPV), and fabrication…
We show that the probability distribution of the error exponent in i.i.d. code ensembles over classical-quantum (CQ) channels with arbitrary output states accumulates above a threshold that is strictly larger than the CQ random coding…
The analysis of the decoding failure rate of the bit-flipping algorithm has received increasing attention. For a binary linear code we consider the minimum number of rows in a parity-check matrix such that the bit-flipping algorithm is able…
A novel recursive list decoding (RLD) algorithm for Reed-Muller (RM) codes based on successive permutations (SP) of the codeword is presented. A low-complexity SP scheme applied to a subset of the symmetry group of RM codes is first…
The generalized Poor-Verdu error lower bound established in [1] for multihypothesis testing is studied in the classical channel coding context. It is proved that for any sequence of block codes sent over the memoryless binary symmetric…
In 1948, Shannon used a probabilistic argument to show the existence of codes achieving a maximal rate defined by the channel capacity. In 1954, Muller and Reed introduced a simple deterministic code construction based on polynomial…
In this paper, we prove that the sub-field images of generalized Reed-Solomon (RS) codes can achieve the symmetric capacity of p-ary memoryless channels. Unlike the totally random linear code ensemble, as a class of maximum distance…
The decoding error probability of codes is studied as a function of their block length. It is shown that the existence of codes with a polynomially small decoding error probability implies the existence of codes with an exponentially small…
A framework for stealth communication with vanishing power (VP) is presented by studying binary symmetric channels. Coding theorems are proved by modifying Gallager's error exponents for VP and by applying resolvability exponents. The…
We present a constraint-coding scheme to correct asymmetric magnitude-$1$ errors in multi-level non-volatile memories. For large numbers of such errors, the scheme is shown to deliver better correction capability compared to known…
Bounds on the reliability function for the discrete memoryless relay channel are derived using the method of types. Two achievable error exponents are derived based on partial decode-forward and compress-forward which are well-known…
In this paper we consider regular low-density parity-check codes over a binary-symmetric channel in the decoding regime. We prove that up to a certain noise threshold the bit-error probability of the bit-sampling decoder converges in mean…
We present an asymptotic limit between correctable and uncor-rectable errors on the Reed-Muller codes of any order. This limit is theoretical and does not depend of any decoding algorithm.
The second-order coding rate of the multiple-input multiple-output (MIMO) quasi-static Rayleigh fading channel is studied. We tackle this problem via an information-spectrum approach and statistical bounds based on recent random matrix…
The {\em binary deletion channel} with deletion probability $d$ ($\text{BDC}_d$) is a random channel that deletes each bit of the input message i.i.d with probability $d$. It has been studied extensively as a canonical example of a channel…
Quantum burst error correction codes (QBECCs) are of great importance to deal with the memory effect in quantum channels. As the most important family of QBECCs, quantum cyclic codes (QCCs) play a vital role in the correction of burst…
A conceptually simple method for derivation of lower bounds on the error exponent of specific families of block codes used on classical-quantum channels with arbitrary signal states over a finite Hilbert space is presented. It is shown that…
We study the following natural question on random sets of points in $\mathbb{F}_2^m$: Given a random set of $k$ points $Z=\{z_1, z_2, \dots, z_k\} \subseteq \mathbb{F}_2^m$, what is the dimension of the space of degree at most $r$…
The classical majority-logic decoder proposed by Reed for Reed-Muller codes RM(r, m) of order r and length 2^m, unfolds in r+1 sequential steps, decoding message symbols from highest to lowest degree. Several follow-up decoding algorithms…
A framework of monomial codes is considered, which includes linear codes generated by the evaluation of certain monomials. Polar and Reed-Muller codes are the two best-known representatives of such codes and can be considered as two extreme…