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This paper studies the performance of block coding on an additive white Gaussian noise channel under different power limitations at the transmitter. Lower bounds are presented for the minimum error probability of codes satisfying maximal…
A linear-programming decoder for \emph{nonbinary} expander codes is presented. It is shown that the proposed decoder has the maximum-likelihood certificate properties. It is also shown that this decoder corrects any pattern of errors of a…
Fault-tolerant quantum computers will depend crucially on the performance of the classical decoding algorithm which takes in the results of measurements and outputs corrections to the errors inferred to have occurred. Machine learning…
The bit-error threshold of the standard ensemble of Low Density Parity Check (LDPC) codes is known to be close to capacity, if there is a non-zero fraction of degree-two bit nodes. However, the degree-two bit nodes preclude the possibility…
Upper and lower bounds on the error probability of linear codes under maximum-likelihood (ML) decoding are shortly surveyed and applied to ensembles of codes on graphs. For upper bounds, focus is put on Gallager bounding techniques and…
We show that duals of certain low-density parity-check (LDPC) codes, when used in a standard coset coding scheme, provide strong secrecy over the binary erasure wiretap channel (BEWC). This result hinges on a stopping set analysis of…
Consider communication over a binary-input memoryless output-symmetric channel with low density parity check (LDPC) codes and maximum a posteriori (MAP) decoding. The replica method of spin glass theory allows to conjecture an analytic…
Most existing works of polar codes focus on the analysis of block error probability. However, in many scenarios, bit error probability is also important for evaluating the performance of channel codes. In this paper, we establish a new…
We introduce a new paradigm for finite precision iterative decoding on low-density parity-check codes over the Binary Symmetric channel. The messages take values from a finite alphabet, and unlike traditional quantized decoders which are…
Binary message-passing decoders for low-density parity-check (LDPC) codes are studied by using extrinsic information transfer (EXIT) charts. The channel delivers hard or soft decisions and the variable node decoder performs all computations…
Cyclic liftings are proposed to lower the error floor of low-density parity-check (LDPC) codes. The liftings are designed to eliminate dominant trapping sets of the base code by removing the short cycles which form the trapping sets. We…
Departing from traditional communication theory where decoding algorithms are assumed to perform without error, a system where noise perturbs both computational devices and communication channels is considered here. This paper studies…
Consider binary linear codes obtained from bipartite graphs as follows. There are~\(k \geq 1\) left nodes each representing a message bit and there are~\(m = m(k)\) right nodes each representing a parity bit, generated from the…
In this work, we analyze efficient window shift schemes for windowed decoding of spatially coupled low-density parity-check (SC-LDPC) codes, which is known to yield close-tooptimal decoding results when compared to full belief propagation…
Assuming iterative decoding for binary erasure channels (BECs), a novel tree-based technique for upper bounding the bit error rates (BERs) of arbitrary, finite low-density parity-check (LDPC) codes is provided and the resulting bound can be…
We consider a broadcast channel with a degraded message set, in which a single transmitter sends a common message to two receivers and a private message to one of the receivers only. The main goal of this work is to find new lower bounds to…
This paper is focused on the performance analysis of binary linear block codes (or ensembles) whose transmission takes place over independent and memoryless parallel channels. New upper bounds on the maximum-likelihood (ML) decoding error…
Neural networks can efficiently encode the probability distribution of errors in an error correcting code. Moreover, these distributions can be conditioned on the syndromes of the corresponding errors. This paves a path forward for a…
Consider the transmission of a polar code of block length $N$ and rate $R$ over a binary memoryless symmetric channel $W$ and let $P_e$ be the block error probability under successive cancellation decoding. In this paper, we develop new…
A new lower bound for the average probability or error for a two-user discrete memoryless (DM) multiple-access channel (MAC) is derived. This bound has a structure very similar to the well-known sphere packing packing bound derived by…