The Constantin-Rao Construction for Binary Assymmetric Error-Correcting Codes

Nhtsl kninvn clwwes of binory Crror.corrcctirlg cocks h:lvc Iwcn dcsiyrcd for usc on symnwtric ch:innels, i.e.. chonnels for which the error prob;lbilitit’s I ~ O snd O -+ I are cqu:il. IIowcvcr. in ccrlvin applications (e.g.. LSI memory protection (l{cf. I). optic:lt c~)lllttttltlic:llit>n (Ref. 6)). tlw observed errors :Irc highly :Isynlnwtric. and the uppropriistc ch:lntwl model moy in f:wl Iw the Z-ckrnncl. in which the trwlsilion O I is impossible. Of course any code cap:lble of correcl ing t errors ~m ii symnwtric clurntwl will also be cspable of correcting I Z.chantwl crrtm; but at present thtre i$ no entirely sotisf:w. ttlry tccllniquc for chxsling direclly with osymnwtric errors. Cotllp:lr; lblc wy to the llCl lGIppa const rwlion (Ref. 5) for symmetric errors, Recently. however. Constnntin 3nd Rno (l{cf. 1) guve 3n ingenious construction for 3 cksss d Ilinary C(UICS c;IpJIIle d correcting a single asymmetric error. Since ,mr orticlc is b:lscd on theirs, we Iwgin will) 3 akcriplion of lltc ~..R. COdCS.