Related papers: Upper Bound on Error Exponent of Regular LDPC Code…
We investigate the relation between the girth and the guaranteed error correction capability of $\gamma$-left regular LDPC codes when decoded using the bit flipping (serial and parallel) algorithms. A lower bound on the number of variable…
There is a known best possible upper bound on the probability of undetected error for linear codes. The $[n,k;q]$ codes with probability of undetected error meeting the bound have support of size $k$ only. In this note, linear codes of full…
Using combinatorial arguments, we determine an upper bound on achievable rates of stabilizer codes used over the quantum erasure channel. This allows us to recover the no-cloning bound on the capacity of the quantum erasure channel, R is…
This paper considers the performance of $(j,k)$-regular low-density parity-check (LDPC) codes with message-passing (MP) decoding algorithms in the high-rate regime. In particular, we derive the high-rate scaling law for MP decoding of LDPC…
For the information transmission a binary symmetric channel is used. There is also another noisy binary symmetric channel (feedback channel), and the transmitter observes without delay all the outputs of the forward channel via that…
We provide a general framework for bounding the block error threshold of a linear code $C\subseteq \mathbb{F}_2^N$ over the erasure channel in terms of its bit error threshold. Our approach relies on understanding the minimum support weight…
Performance evaluation of particular channel coding has been a significant topic in coding theory, often involving the use of bounding techniques. This paper focuses on the new family of capacity-achieving codes, Spinal codes, to provide a…
Forward error correcting (FEC) codes are used in many communication standards with a wide range of re quirements. FEC codes should work close to capacity, achieve low error floors, and have low decoding complexity. In this paper, we propose…
We consider spatially coupled code ensembles. A particular instance are convolutional LDPC ensembles. It was recently shown that, for transmission over the memoryless binary erasure channel, this coupling increases the belief propagation…
We prove that, for the binary erasure channel (BEC), the polar-coding paradigm gives rise to codes that not only approach the Shannon limit but do so under the best possible scaling of their block length as a~function of the gap to…
This paper studies the concentration properties of random codes. Specifically, we show that, for discrete memoryless channels, the error exponent of a randomly generated code with pairwise-independent codewords converges in probability to…
We investigate the privacy amplification problem in which Eve can observe the uniform binary source through a binary erasure channel (BEC) or a binary symmetric channel (BSC). For this problem, we derive the so-called expurgation exponent…
For the discrete-time additive white generalized Gaussian noise channel with a generalized input power constraint, with the respective shape and power parameters >= 1, we derive an upper bound on the optimal block error exponent. Explicit…
Locally repairable codes (LRCs) were originally introduced to enable efficient recovery from erasures in distributed storage systems by accessing only a small number of other symbols. While their structural properties-such as bounds and…
In this paper, we will present an analysis on the fault erasure BP decoders based on the density evolution. In the fault BP decoder, messages exchanged in a BP process are stochastically corrupted due to unreliable logic gates and…
Protograph low-density-parity-check (LDPC) are considered to design near-capacity low-rate codes over the binary erasure channel (BEC) and binary additive white Gaussian noise (BIAWGN) channel. For protographs with degree-one variable nodes…
In continuation to an earlier work, where error exponents of typical random codes were studied in the context of general block coding, with no underlying structure, here we carry out a parallel study on typical random, time-varying trellis…
This paper considers the problem of covert communication with mismatched decoding, in which a sender wishes to reliably communicate with a receiver whose decoder is fixed and possibly sub-optimal, and simultaneously to ensure that the…
This paper shows that the logarithm of the epsilon-error capacity (average error probability) for n uses of a discrete memoryless channel is upper bounded by the normal approximation plus a third-order term that does not exceed 1/2 log n +…
We present a method for estimating the undetected error rate when a cyclic redundancy check (CRC) is performed on the output of the decoder of short low-density parity-check (LDPC) codes. This system is of interest for telecommand links,…