On Tanner Graph Error-Detection of Some Codes due to (123)/ (132)-Avoiding Patterns of AUNU Numbers

Abstract

We consider some of the codes generated due to the AUNU patterns as studied earlier by the authors (the [5 3 2] linear code, [7 4 2]-linear code and the [14 8 3] codes) . The Parity check matrices of these codes are obtained and used in constructing their Tanner graphs. A Tanner graph has n variable nodes, corresponding to the code bits of the codeword, and m check nodes that represents the parity check equations. An assignment of the code bits of a received vector is now known to be a valid code word if all the parity check equations from the Tanner graph are satisfied otherwise, an error is detected. Moreover, other code properties such as the regularity or otherwise of these codes are also determined from such Tanner graphs.