Related papers: On Index Codes for Interlinked Cycle Structured Si…
In this paper, the analysis of the performance of the concatenation of a short polar code with an outer binary linear block code is addressed from a distance spectrum viewpoint. The analysis targets the case where an outer cyclic code is…
Generalized Tanner graphs have been implicitly studied by a number of authors under the rubric of generalized parity-check matrices. This work considers the conditioning of binary hidden variables in such models in order to break all cycles…
An index code is said to be locally decodable if each receiver can decode its demand using its side information and by querying only a subset of the transmitted codeword symbols instead of observing the entire codeword. Local decodability…
We present algorithms for initializing a convolutional network coding scheme in networks that may contain cycles. An initialization process is needed if the network is unknown or if local encoding kernels are chosen randomly. During the…
Cycle codes are a special case of low-density parity-check (LDPC) codes and as such can be decoded using an iterative message-passing decoding algorithm on the associated Tanner graph. The existence of pseudo-codewords is known to cause the…
This paper analyzes the distribution of cycle lengths in turbo decoding and low-density parity check (LDPC) graphs. The properties of such cycles are of significant interest in the context of iterative decoding algorithms which are based on…
We propose a novel decoding algorithm for staircase codes which reduces the effect of undetected component code miscorrections. The algorithm significantly improves performance, while retaining a low-complexity implementation suitable for…
While constructing polar codes for successive-cancellation decoding can be implemented efficiently by sorting the bit-channels, finding optimal polar codes for cyclic-redundancy-check-aided successive-cancellation list (CA-SCL) decoding in…
A class of linear block codes which simultaneously generalizes Gabidulin codes and a class of skew cyclic codes is defined. For these codes, both a Hartmann-Tzeng-like bound and a Roos-like bound, with respect to their rank distance, are…
We establish necessary and sufficient conditions for the existence of a decomposition of a complete multigraph into edge-disjoint cycles of specified lengths, or into edge-disjoint cycles of specified lengths and a perfect matching.
Background Nucleotide sequences contain multiple codes responsible for organism's functioning and structure. They can be investigated by various signal processing methods. These techniques are well suited for indication of frequently…
Cyclic codes are a subclass of linear codes and have applications in consumer electronics, data storage systems, and communication systems as they have efficient encoding and decoding algorithms. In this paper, almost perfect nonlinear…
This paper is concerned with list decoding of $2$-interleaved binary alternant codes. The principle of the proposed algorithm is based on a combination of a list decoding algorithm for (interleaved) Reed-Solomon codes and an algorithm for…
In this work we propose an encoding and decoding framework for staircase codes based on non-systematic polar codes as component codes. The staircase structure allows for efficient parallelized decoding, while the polar component codes allow…
An efficient decoding algorithm for horizontally u-interleaved LRPC codes is proposed and analyzed. Upper bounds on the decoding failure rate and the computational complexity of the algorithm are derived. It is shown that interleaving…
A problem of index coding with side information was first considered by Y. Birk and T. Kol (IEEE INFOCOM, 1998). In the present work, a generalization of index coding scheme, where transmitted symbols are subject to errors, is studied.…
We consider the problem of coding over the multi-user Interference Channel (IC). It is well-known that aligning the interfering signals results in improved achievable rates in certain setups involving more than two users. We argue that in…
In this paper, we investigate the problem of recovering source information from an incomplete set of network coded data. We first study the theoretical performance of such systems under maximum a posteriori (MAP) decoding and derive the…
We recall several known results about minimally 2-connected graphs, and show that they all follow from a decomposition theorem. Starting from an analogy with critically 2-connected graphs, we give structural characterizations of the classes…
An iterative decoding algorithm for convolutional codes is presented. It successively processes $N$ consecutive blocks of the received word in order to decode the first block. A bound is presented showing which error configurations can be…