This paper gives some theory and design of efficient binary block codes capable of correcting the deletion and/or insertion of the symbol "0" in a received sequence. This problem is shown to be equivalent to the efficient design of some L1 metric asymmetric error control codes over the natural alphabet, N. Optimal non-systematic and systematic code designs are given. In particular, given t in N, a recursive method is given to encode k in N information bits into a systematic code of length n=k+tcdotlog_{2}k+O(loglog k), capable of correcting at most t deletions and/or insertions of 0's in every received word. Decoding can be efficiently performed by algebraic means with the Extended Euclidean Algorithm (EEA).
On Deletion/Insertion of 0’s Errors and Asymmetric Error Control Codes (ad invito)
Tallini, Luca G.;
2018-01-01
Abstract
This paper gives some theory and design of efficient binary block codes capable of correcting the deletion and/or insertion of the symbol "0" in a received sequence. This problem is shown to be equivalent to the efficient design of some L1 metric asymmetric error control codes over the natural alphabet, N. Optimal non-systematic and systematic code designs are given. In particular, given t in N, a recursive method is given to encode k in N information bits into a systematic code of length n=k+tcdotlog_{2}k+O(loglog k), capable of correcting at most t deletions and/or insertions of 0's in every received word. Decoding can be efficiently performed by algebraic means with the Extended Euclidean Algorithm (EEA).I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
