Decoding a Perturbed Sequence Generated by an LFSR

Autor(es)

Cardell, Sara D. ; Climent, Joan-Josep ; Roca, Alicia ; Barbero, AI ; Skachek, V ; Ytrehus, O

• Tipo de documento: Artigo Científico
• Fonte: CODING THEORY AND APPLICATIONS, ICMCTA 2017; v. 10495, p. 10-pg., 2017-01-01.

Resumo

Given a sequence of bits produced by a linear feedback shift register (LFSR), the Berlekamp-Massey algorithm finds a register of minimal length able to generate the sequence. The situation is different when the sequence is perturbed; for instance, when it is sent through a transmission channel. LFSRs can be described as autonomous systems. A perturbed sequence of bits generated by an LFSR can be interpreted as a codeword in the binary linear code generated by the corresponding observability matrix. The problem of finding the original sequence can then be stated as the decoding problem, "given the received codeword, find the information transmitted". We propose two decoding algorithms, one based on a brute force attack and the other one based on the representation technique of the syndromes introduced by Becker, Joux, May, and Meurer (2012). (AU)

• Processo FAPESP: 15/07246-0 - Construção, decodificação e implementação de códigos F_q lineares. Performance de códigos SPC produto e criptoanalise de contração de geradores.
• Beneficiário: Sara Díaz Cardell
• Modalidade de apoio: Bolsas no Brasil - Pós-Doutorado