论文信息 - Formalization of Reed-Solomon codes and progress report on formalization of LDPC codes

Formalization of Reed-Solomon codes and progress report on formalization of LDPC codes

Error-correcting codes make possible reliable communication over noisy channels. One way to guarantee the correct implementation of error-correcting codes is to use formal verification. This requires in particular the formalization of the mathematical theory of error-correcting codes. This has been made possible by recent advances in the formalization of mathematics using proof-assistants. In this paper, we discuss formalization of linear error-correcting codes: we introduce a formalization of cyclic codes and Euclidean decoding that we apply to Reed-Solomon codes, and we discuss the advanced topic of LDPC codes.

[1] Rüdiger L. Urbanke,et al. Modern Coding Theory , 2008 .

[2] Andrei V. Kelarev,et al. The Theory of Information and Coding , 2005 .

[3] Rüdiger L. Urbanke,et al. The capacity of low-density parity-check codes under message-passing decoding , 2001, IEEE Trans. Inf. Theory.

[4] Jeremy Avigad,et al. A Machine-Checked Proof of the Odd Order Theorem , 2013, ITP.

[5] Robert J. McEliece,et al. The Theory of Information and Coding , 1979 .

[6] Lawrence C. Paulson,et al. A Pragmatic Approach to Extending Provers by Computer Algebra - with Applications to Coding Theory , 1999, Fundam. Informaticae.

[7] Jacques Garrigue,et al. Formalization of Error-Correcting Codes: From Hamming to Modern Coding Theory , 2015, ITP.

[8] Enrico Tassi,et al. A Small Scale Reflection Extension for the Coq system , 2008 .