2012/06/11 by Masoud Alipour, Omid Etesami, Alipour, Masoud +5
Biochemistry, Genetics and Molecular Biology · Computer Science · Mathematics · #Cellular Automata and Applications #DNA and Biological Computing #Error Correcting Code Techniques #FOS: Computer and information sciences #Information Theory (cs.IT) #cs.IT #math.IT
paper · pdf · doi:10.48550/arxiv.1206.2276
First draft
arxiv created 2012/06/11 · openalex publication_date 2012/06/11 · arxiv updated 2012/06/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider irregular product codes.In this class of codes, each codeword is represented by a matrix. The entries in each row (column) of the matrix should come from a component row (column) code. As opposed to (standard) product codes, we do not require that all component row codes nor all component column codes be the same. As we will see, relaxing this requirement can provide some additional attractive features including 1) allowing some regions of the codeword be more error-resilient 2) allowing a more refined spectrum of rates for finite-lengths and improved performance in some of these rates 3) more interaction between row and column codes during decoding. We study these codes over erasure channels. We find that for any 0 < ε< 1, for many rate distributions on component row codes, there is a matching rate distribution on component column codes such that an irregular product code based on MDS codes with those rate distributions on the component codes has asymptotic rate 1 - ε and can decode on erasure channels (of alphabet size equal the alphabet size of the component MDS codes) with erasure probability < ε.