We investigate image steganography under re-encoding of images. After a secret message or a digital watermark is embedded into a jpeg image, quite frequently the image is re-encoded with a different quality factor. We model this re-encoding as a noisy communication channel with respect to the embedded message, and derive the corresponding error model. We present an error-correcting code that al...

Methods of finding good quantum error correcting codes are discussed, and many example codes are presented. The recipe C⊥ 2 ⊆ C1, where C1 and C2 are classical codes, is used to obtain codes for up to 16 information qubits with correction of small numbers of errors. The results are tabulated. More efficient codes are obtained by allowing C1 to have reduced distance, and introducing sign changes...

The conservation of genetic information through the ages can not be explained unless one assumes the existence of genomic error-correcting codes, our main hypothesis. Shielding by phenotypic membranes does not protect the genomes against radiations and their own quantum indeterminism. The cumulated errors then make the genomic memory ephemeral at the time scale of geology. Only means intrinsic ...

Quantum error-correcting codes have attracted much attention. Among many research articles, the most general and systematic construction is the so called stabilizer code construction [6] or additive code construction [2], which constructs a quantum error-correcting code as an eigenspace of an Abelian subgroup S of the error group. Thereafter Calderbank et al. [3] proposed a construction of S fr...

Multi-level cell (MLC) NAND flash memories are very popular storage media because of their power efficiency and big storage capacity. This paper proposes to use nonlinear t-error-correcting codes to replace linear BCH codes for error detection and correction in MLC NAND flash memories. Compared to linear BCH codes with the same bit-error correcting capability t, the proposed codes have the adva...

In this paper, we present an open source Error-Correcting Output Codes (ECOC) library. The ECOC framework is a powerful tool to deal with multi-class categorization problems. This library contains both state-of-the-art coding (one-versus-one, one-versus-all, dense random, sparse random, DECOC, forest-ECOC, and ECOC-ONE) and decoding designs (hamming, euclidean, inverse hamming, laplacian, β-den...

In today's lecture, we will discuss the application of expander graphs to error-correcting codes. More specifically, we will describe the construction of linear-time decodable expander codes due to Sipser and Spielman. We begin with some preliminaries on error-correcting codes. (Several of the proofs presented in this lecture are adapted from the lecture notes of Venkatesan Guruswami's course o...

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The field of channel coding started with Claude Shannon’s 1948 landmark paper. Fifty years of efforts and invention have finally produced coding schemes that closely approach Shannon’s channel capacity limit on AWGN channels, both power-limited and band-limited. Similar gains are being achieved in other important applications, such as wireless channels. This course is divided in two parts. In t...