Theoretical analysis of the error correction performance of majority-logic-like vector symbol codes

The average codeword success probability of the majority-logic-like vector symbol (MLLVS) code is derived for the following two cases: (1) single-pass decoding and (2) upper bound of multipass decoding, when the received word has more than (J-1) symbol errors, where J is the number of check sum equations. The MLLVS code has been simulated by Metzner (1996), and it was concluded that the average error correcting capability of MLLVS codes exceed the decoding capability of Reed-Solomon codes, but is achieved with less complexity. Additionally, for codes that have larger structures, the error correcting capability is sustained even further with a high probability of decoding success through multipass decoding procedures. The mathematical derivations of the error correction performance beyond (J-1) symbol errors serve as theoretical proof of the MLLVS code error correcting capability that was shown only through simulation results until now by Metzner. One characteristic feature of this derivation is that it does not assume any specific inner code usage, enabling the derived decoding probability equations to be easily applied to any inner code selected, of a concatenated coding structure