A Method of Examining Orchard Codes for Minimum Hamming Distance Five

Orchard codes are linear, systematic tree codes of rate and infinite block length. Calculation of parity bits is over prior parity bits, as well as prior information bits. The memory needed to encode is about half that of comparable convolutional self-orthogonal codes. After a brief review of recent work involving two-error-correcting orchard codes [1], [2], the authors present a method of analysis of orchard codes to establish whether minimal distance criteria are met. It is assumed that parity is taken over three bits per track. The code introduced by Scott and Goetschel [1], and a truncated version of the code designed by Shiozaki [2], are then analyzed. New orchard codes, designed on the basis of the analysis method, are presented. The method is extendible to codes designed to correct more than two errors, although extension beyond three errors is computationally intensive.