Reed-Muller codes are among the most important classes of locally correctable codes. Currently local decoding of Reed-Muller codes is based on decoding on lines or quadratic curves to recover one single coordinate. To recover multiple coordinates simultaneously, the naive way is to repeat the local decoding for recovery of a single coordinate. This decoding algorithm might be more expensive, i....

In this paper, two new hybrid algorithms are proposed for decoding Low Density Parity Check (LDPC) codes. Original version of the proposed algorithms named Search Based Weighted Multi Bit Flipping (SWMBF). The main idea of these algorithms is flipping variable multi bits in each iteration, change in which leads to the syndrome vector with least hamming weight. To achieve this, the proposed algo...

In this paper a new patch-based digital signature (DS) is proposed. The proposed approach similar to steganography methods hides the secure message in a host image. However, it uses a patch-based key to encode/decode the data like cryptography approaches. Both the host image and key patches are randomly initialized. The proposed approach consists of encoding and decoding algorithms. The encodin...

1 Department of Telematics, Norwegian University of Science and Technology (NTNU), Trondheim, NORWAY, {danilog, simonas, hakoja}@item.ntnu.no 2 “Ss Cyril and Methodius” University, Faculty of Computer Science and Engineering (FINKI), Skopje, MACEDONIA [email protected] 3 Saint Petersburg State University of Aerospace Instrumentation, Saint Petersburg, RUSSIA, [email protected] Abstrac...

This thesis presents a complete VLSI design of improved low complexity chase (LCC) decoders for Reed-Solomon (RS) codes. This is the first attempt in published research that implements LCC decoders at the circuit level. Based on the joint algorithm research with University of Hawaii, we propose several new techniques for complexity reduction in LCC decoders and apply them in the VLSI design for...

This thesis presents a complete VLSI design of improved low complexity chase (LCC) decoders for Reed-Solomon (RS) codes. This is the first attempt in published research that implements LCC decoders at the circuit level. Based on the joint algorithm research with University of Hawaii, we propose several new techniques for complexity reduction in LCC decoders and apply them in the VLSI design for...

The security of code-based cryptography relies primarily on the hardness generic decoding with linear codes. best algorithms are all improvements an old algorithm due to Prange: they known under name information set decoders (ISD). A while ago, a which does not belong this family was proposed: statistical decoding. It is randomized that requires computation large parity-checks moderate weight, ...

Encoders and decoders for variable-length codes such as Huffman Codes can be costly to implement. This paper describes low-cost encoder and decoder for binary variable-length codes that is simple to implement when decoding speed is not an issue.

We consider the following game introduced by Chung, Graham, and Leighton in [Chung et al. 01]. One player, A, picks k > 1 secrets from a universe of N possible secrets, and another player, B, tries to gain as much information about this set as possible by asking binary questions f : [N ] −→ {0, 1}. Upon receiving a question f , A adversarially chooses one of her k secrets, and answers f accordi...