Improving success probability and embedding efficiency in code based steganography

For stegoschemes arising from error correcting codes, embedding depends on a decoding map for the corresponding code. As decoding maps are usually not complete, embedding can fail. We propose a method to ensure or increase the probability of embedding success for these stegoschemes. This method is based on puncturing codes. We show how the use of punctured codes may also increase the embedding efficiency of the obtained stegoschemes

Functional diagnosability and recovery from massive faults in digital systems Quarterly progress reports, 17 May - 16 Nov. 1970 /final/

Diagnosability and recovery from massive faults in digital system

A Microprocessor based hybrid system for digital error correction

The design of a microprocessor based hybrid system for digital error correction is presented. It is shown that such a system allows for implementation of several cyclic codes at a variety of throughput rates providing variable degrees of error correction depending on current user requirements. The theoretical basis for encoding and decoding of binary BCH codes is reviewed. Design and implementation of system hardware and software are described. A method for injection of independent bit errors with controllable statistics into the system is developed, and its accuracy verified by computer simulation. This method of controllable error injection is used to test performance of the designed system. In analysis, these results demonstrate the flexibility of operation provided by the hybrid nature of the system. Finally, potential applications and modifications are presented to reinforce the wide applicability of the system described in this thesis

Permutation Decoding and the Stopping Redundancy Hierarchy of Cyclic and Extended Cyclic Codes

We introduce the notion of the stopping redundancy hierarchy of a linear block code as a measure of the trade-off between performance and complexity of iterative decoding for the binary erasure channel. We derive lower and upper bounds for the stopping redundancy hierarchy via Lovasz's Local Lemma and Bonferroni-type inequalities, and specialize them for codes with cyclic parity-check matrices. Based on the observed properties of parity-check matrices with good stopping redundancy characteristics, we develop a novel decoding technique, termed automorphism group decoding, that combines iterative message passing and permutation decoding. We also present bounds on the smallest number of permutations of an automorphism group decoder needed to correct any set of erasures up to a prescribed size. Simulation results demonstrate that for a large number of algebraic codes, the performance of the new decoding method is close to that of maximum likelihood decoding.Comment: 40 pages, 6 figures, 10 tables, submitted to IEEE Transactions on Information Theor

Nonlinear, nonbinary cyclic group codes

New cyclic group codes of length 2(exp m) - 1 over (m - j)-bit symbols are introduced. These codes can be systematically encoded and decoded algebraically. The code rates are very close to Reed-Solomon (RS) codes and are much better than Bose-Chaudhuri-Hocquenghem (BCH) codes (a former alternative). The binary (m - j)-tuples are identified with a subgroup of the binary m-tuples which represents the field GF(2 exp m). Encoding is systematic and involves a two-stage procedure consisting of the usual linear feedback register (using the division or check polynomial) and a small table lookup. For low rates, a second shift-register encoding operation may be invoked. Decoding uses the RS error-correcting procedures for the m-tuple codes for m = 4, 5, and 6

Constructions of Rank Modulation Codes

Rank modulation is a way of encoding information to correct errors in flash memory devices as well as impulse noise in transmission lines. Modeling rank modulation involves construction of packings of the space of permutations equipped with the Kendall tau distance. We present several general constructions of codes in permutations that cover a broad range of code parameters. In particular, we show a number of ways in which conventional error-correcting codes can be modified to correct errors in the Kendall space. Codes that we construct afford simple encoding and decoding algorithms of essentially the same complexity as required to correct errors in the Hamming metric. For instance, from binary BCH codes we obtain codes correcting $t$ Kendall errors in $n$ memory cells that support the order of $n!/(\log_2n!)^t$ messages, for any constant $t= 1,2,...$ We also construct families of codes that correct a number of errors that grows with $n$ at varying rates, from $\Theta(n)$ to $\Theta(n^{2})$. One of our constructions gives rise to a family of rank modulation codes for which the trade-off between the number of messages and the number of correctable Kendall errors approaches the optimal scaling rate. Finally, we list a number of possibilities for constructing codes of finite length, and give examples of rank modulation codes with specific parameters.Comment: Submitted to IEEE Transactions on Information Theor