Related papers: Rates of linear codes with low decoding error prob…
Storage codes on graphs are an instance of \emph{codes with locality}, which are used in distributed storage schemes to provide local repairability. Specifically, the nodes of the graph correspond to storage servers, and the neighbourhood…
In this paper, we show how to construct a factor graph from a network code. This provides a systematic framework for decoding using message passing algorithms. The proposed message passing decoder exploits knowledge of the underlying…
For every p in (0,1/2), we give an explicit construction of binary codes of rate approaching "capacity" 1-H(p) that enable reliable communication in the presence of worst-case additive errors}, caused by a channel oblivious to the codeword…
We develop a framework for linear-programming (LP) decoding of non-binary linear codes over rings. We prove that the resulting LP decoder has the `maximum likelihood certificate' property, and we show that the decoder output is the lowest…
We obtain exact expressions for the asymptotic behaviour of the average probability of the block decoding error for ensembles of regular low density parity check error correcting codes, by employing diagrammatic techniques. Furthermore, we…
This paper considers a base station that delivers packets to multiple receivers through a sequence of coded transmissions. All receivers overhear the same transmissions. Each receiver may already have some of the packets as side…
A low-density parity-check (LDPC) code is a linear block code described by a sparse parity-check matrix, which can be efficiently represented by a bipartite Tanner graph. The standard iterative decoding algorithm, known as belief…
In this study we consider rateless coding over discrete memoryless channels (DMC) with feedback. Unlike traditional fixed-rate codes, in rateless codes each codeword is infinitely long, and the decoding time depends on the confidence level…
We consider the problem of finding all allowed edges in a bipartite graph $G=(V,E)$, i.e., all edges that are included in some maximum matching. We show that given any maximum matching in the graph, it is possible to perform this…
Error correction codes are an integral part of communication applications, boosting the reliability of transmission. The optimal decoding of transmitted codewords is the maximum likelihood rule, which is NP-hard due to the curse of…
We consider the dynamics of belief propagation decoding of spatially coupled Low-Density Parity-Check codes. It has been conjectured that after a short transient phase, the profile of "error probabilities" along the spatial direction of a…
This paper considers rateless network error correction codes for reliable multicast in the presence of adversarial errors. Most existing network error correction codes are designed for a given network capacity and maximum number of errors…
We consider the problem of polar coding for transmission over $m$-user multiple access channels. In the proposed scheme, all users encode their messages using a polar encoder, while a joint successive cancellation decoder is deployed at the…
Forward Error Correction (FEC) is used ubiquitously in the communication pipeline. We explore noncooperative decoding where we aim to recover the code rate of a linear block code. We present a metric to characterize the quality of the code…
We compare the performance of short-length linear binary codes on the binary erasure channel and the binary-input Gaussian channel. We use a universal decoder that can decode any linear binary block code: Gaussian-elimination based…
Prange's information set algorithm is a decoding algorithm for arbitrary linear codes. It decodes corrupted codewords of any $\mathbb{F}_2$-linear code $C$ of message length $n$ up to relative error rate $O(\log n / n)$ in…
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…
This paper considers a binary channel with deletions and insertions, where each input bit is transformed in one of the following ways: it is deleted with probability d, or an extra bit is added after it with probability i, or it is…
In this paper, we propose a linear representation of BCJR maximum a posteriori probability (MAP) decoding of a rate 1/2 convolutional code (CC), referred to as the linear MAP decoding (LMAP). We discover that the MAP forward and backward…
We construct constant-sized ensembles of linear error-correcting codes over any fixed alphabet that can correct a given fraction of adversarial erasures at rates approaching the Singleton bound arbitrarily closely. We provide several…