On the theory of binary asymmetric error correcting codes

Gallager error-correcting codes for binary asymmetric channels

Abstract. We derive critical noise levels for Gallager codes on asymmetric channels as a function of the input bias and the temperature. Using a statistical mechanics approach we study the space of codewords and the entropy in the various decoding regimes. We further discuss the relation of the convergence of the message passing algorithm with the endogenous property and complexity, characteriz...

Asymmetric quantum error correcting codes

HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau...

Theory of Error - Correcting Codes

The field of channel coding started with Claude Shannon’s 1948 landmark paper. Fifty years of efforts and invention have finally produced coding schemes that closely approach Shannon’s channel capacity limit on AWGN channels, both power-limited and band-limited. Similar gains are being achieved in other important applications, such as wireless channels. This course is divided in two parts. In t...

New single asymmetric error-correcting codes

New single asymmetric error-correcting codes are proposed. These codes are better than existing codes when the code length n is greater than 10, except for n = 12 and n = 15. In many cases one can construct a code C containing at least d2=ne codewords. It is known that a code with jCj d2=(n + 1)e can be easily obtained. It should be noted that the proposed codes for n = 12 and n = 15 are also t...

Two New Four-Error-Correcting Binary Codes