Abstract: A method and apparatus for improving burst error correction. The method and apparatus involve transmitting block codes with interleaving, and predicting a burst error in the received block codes. Burst error prediction includes decoding received block codes and determining if the decoding is successful. The method includes receiving a code having an error correction capability, an erasure detection capability and a burst error length associated with it. A decoding step is performed to find an error in the code. The error has a length associated with it. The decoding is successful if the error length found is less than twice the error correction capability. If an initial decode attempt is not successful, then a burst error length is associated with the code and another decode is performed. The burst error length has an initial value that is less than the error correction capability. The burst error length is incremented by a predetermined amount after each unsuccessful decode until the burst error length exceeds twice the error correction capability, at which point the decode is assumed to have failed.

Abstract: A formal treatment is presented for Al Jabri's (see IEE Electronics Letters, vol.32, no.24, p.2226-7, 1996 and 4th International Symposium on Communication Theory and Applications, Ambleside, Lake District, UK, 13-18, p.197-200, 1997) attack to reconstruct the permutation in secret-key schemes based on single-burst correcting codes. An extension of that technique to attack secret-key cryptosystems based on multi-burst correcting codes is presented and shown to be effective. A new encryption scheme is proposed, using burst-error correcting codes and adaptive permutations, which is resistant to known attacks and is specially tailored to counter Al Jabri's attack.

Abstract: We explore the design of quantum error-correcting codes for cases where the decoherence events of qubits are correlated. In particular, we consider the case where only spatially contiguous qubits decohere, which is analogous to the case of burst errors in classical coding theory. We present several different efficient schemes for constructing families of such codes. For example, one can find one-dimensional quantum codes of length n=13 and 15 that correct burst errors of width b<3; as a comparison, a random-error correcting quantum code that corrects t=3 errors must have length n/spl ges/17. In general, we show that it is possible to build quantum burst-correcting codes that have near optimal dimension. For example, we show that for any constant b, there exist b-burst-correcting quantum codes with length n, and dimension k=n-log n-O(1); as a comparison, the Hamming bound for the case with t (constant) random errors yields k/spl les/n-tlog n+O(1).