Decoding random linear codes is a well studied problem with many applications in complexity theory and cryptography. The security of almost all coding and LPN/LWE-based schemes relies on the assumption that it is hard to decode random linear codes. Recently, there has been progress in improving ...
Although this phenomenon has been implied by the second order analysis of the coding rate as n goes to ∞ [1], [12]– =-=[15]-=- , the inequalities (2.10) and (2.11) allow us to demonstrate this for specific values of n and for random linear codes based on Gallager parity check ...
The best attacks known against this system are generic decoding attacks that treat McEliece’s hidden binary Goppa codes as random linear codes. A standard conjecture is that the best possiblew-error-decoding attacks against random linear codes of dimensionkand lengthntake time 2(α(R,W) +...
Keywords. Linear codes, decoding of (random) linear codes, sparse solutions to under- determined systems, 1 minimization, basis pursuit, duality in optimization, linear pro- gramming, restricted orthonormality, principal angles, Gaussian random matrices, singular values of random matrices. Acknowledgmen...
It is widely recognized that one of the most significant contributions to coding theory is the invention of Low-Density Parity-Check (LDPC) codes by Gallager in the early 1960s[1,2]. Yet, rather than a family of codes,Gallager invented a new method of decoding linear codes, by using iter...
By scaling and rounding we can easily transform these results to obtain polynomialtime decodable random linear codes with polynomial-sized alphabets tolerating any ρ < ρ∗ ≈ 0.239 fraction of arbitrary errors. In the context of privacy-preserving datamining our results say that any privacy ...
In addition, the agent assumed an ambiguous environment in which the reward probabilities are fluctuated by a random walk as $$w_{i,t} = w_{i,t - 1} + \sigma _w\xi _{i,t},$$ (11) where t, \(\xi _{i,t}\), and \(\sigma _w\) denote the trial of the two-choice ...
P1, P2 and P3 represent the probabilities that two distinct source sequences (differing in the value of one or both source nodes) are mapped by the network code to the same observed sequence at the sink; note that with a random linear network code, the probabilities are unchanged for any ...
Goppa codes are relatively easy to decode, but distinguishing them from a random linear code is considered difficult—this indistinguishability forms the basis of their use in McEliece cryptosystems, since decoding random linear codes is believed to be hard. The keys created can be a public and...
The general concepts of iterative turbo decoding utilizing the MAP and SOVA algorithms are disclosed by Bahl et al. in “Optimal decoding of linear codes for minimizing symbol error rate,” IEEE Trans. Inform. Theory, vol. IT-20, pp. 284-287, March 1974; by Pietrobon in “Implementation an...