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Raptor codes are rateless codes that achieve the capacity on the binary erasure channels. However the maximum degree of optimal output degree distribution is unbounded. This leads to a computational complexity problem both at encoders and…
In this paper, we generalize the well-known index coding problem to exploit the structure in the source-data to improve system throughput. In many applications, the data to be transmitted may lie (or can be well approximated) in a…
Generalized quasi-cyclic (GQC) codes form a natural generalization of quasi-cyclic (QC) codes. They are viewed here as mixed alphabet codes over a family of ring alphabets. Decomposing these rings into local rings by the Chinese Remainder…
Generalized Reed-Solomon (RS) codes are a common choice for efficient, reliable error correction in memory and communications systems. These codes add $2t$ extra parity symbols to a block of memory, and can efficiently and reliably correct…
Distributed storage systems that deploy erasure codes can provide better features such as lower storage overhead and higher data reliability. In this paper, we focus on fractional repetition (FR) codes, which are a class of storage codes…
Subspace codes are collections of subspaces of a projective space such that any two subspaces satisfy a pairwise minimum distance criterion. Recent results have shown that it is possible to construct optimal $(5,3)$ subspace codes from…
Error correction plays a major role in the reconciliation of continuous variable quantum key distribution (CV-QKD) and greatly affects the performance of the system. CV-QKD requires error correction codes of extremely low rates and high…
Spatially-coupled low-density parity-check codes attract much attention due to their capacity-achieving performance and a memory-efficient sliding-window decoding algorithm. On the other hand, the encoder needs to solve large linear…
Secure codes are widely-studied combinatorial structures which were introduced for traitor tracing in broadcast encryption. To determine the maximum size of such structures is the main research objective. In this paper, we investigate the…
An alternative method for collaborative decoding of interleaved Reed-Solomon codes as well as Gabidulin codes for the case of high interleaving degree is proposed. As an example of application, simulation results are presented for a…
In this letter we present a new construction of interleavers for turbo codes from 3-regular Hamiltonian graphs. The interleavers can be generated using a few parameters, which can be selected in such a way that the girth of the interleaver…
We consider sparse superposition codes (SPARCs) over complex AWGN channels. Such codes can be efficiently decoded by an approximate message passing (AMP) decoder, whose performance can be predicted via so-called state evolution in the…
A framework for linear-programming (LP) decoding of nonbinary linear codes over rings is developed. This framework facilitates linear-programming based reception for coded modulation systems which use direct modulation mapping of coded…
Products codes (PCs) are conventionally decoded with efficient iterative bounded-distance decoding (iBDD) based on hard-decision channel outputs which entails a performance loss compared to a soft-decision decoder. Recently, several hybrid…
In this article we see quasi-cyclic codes as block cyclic codes. We generalize some properties of cyclic codes to quasi-cyclic ones such as generator polynomials and ideals. Indeed we show a one-to-one correspondence between l-quasi-cyclic…
Recently, asynchronous coarse-space correction has been achieved within both the overlapping Schwarz and the primal Schur frameworks. Both additive and multiplicative corrections have been discussed. In this paper, we address some…
We consider probabilistic amplitude shaping (PAS) as a means of increasing the spectral efficiency of fiber-optic communication systems. In contrast to previous works in the literature, we consider probabilistic shaping with hard decision…
SC-LDPC codes with sub-block locality can be decoded locally at the level of sub-blocks that are much smaller than the full code block, thus providing fast access to the coded information. The same code can also be decoded globally using…
In this work, lossy distributed compression of pairs of correlated sources is considered. Conventionally, Shannon's random coding arguments -- using randomly generated unstructured codebooks whose blocklength is taken to be asymptotically…
Every better quasi-order codifies a Borel graph that does not contain a copy of the shift graph. It is known that there is a better quasi-order that codes a Borel graph with infinite Borel chromatic number, though one has yet to be…