Analysis of the error correction performance of majority-logic-like vector symbol codes and applications in diversity combining systems

In this dissertation, the average code word success probability of the majority-logic-like vector symbol (MLLVS) code is derived, and the performance of macrodiversity combining over concatenated BCH inner codes and MLLVS codes within lognormally shadowed Rayleigh fading channels are analyzed.; In the first part, the single pass decoding and multi-pass decoding upper bound error correction performance of the MLLVS code is derived for the case when the received code word has more than (J-1) symbol errors, where J is the number of check sum equations. The MLLVS code has been simulated, and it was concluded that MLLVS codes exceed Reed-Solomon codes in decoding performance. This advantage in coding gain comes with the feature that the decoder structure and decoding procedures of the MLLVS codes are simpler compared to Reed-Solomon codes. Additionally, for codes that have larger structures, the error correcting capability is sustained even further with a higher probability of decoding success through multi-pass decoding procedures. The mathematical derivations of the error correcting performance beyond (J-1) symbol errors serves as a theoretical proof of the MLLVS code error correcting capability that was shown only through simulation until now. One characteristic of this derivation is that it does not assume any specific inner code usage, meaning that the derived decoding probability equations can be easily applied to any inner code selected, of a concatenated coding structure.; Secondly, the performance of concatenated coding with macrodiversity symbol combining over lognormally shadowed Rayleigh fading channels are analyzed. The concatenated code consists of a double error correcting BCH inner code and MLLVS outer codes. Continuous phase modulation is used with microscopic combining at the receiving stations before error control decoding and macrodiversity combining is performed. The microdiversity model assumes two combining receivers with selection diversity followed by BCH inner decoding, where the macrodiversity model assumes three combining stations participating in the symbol combining before outer code decoding. Results indicate that at the 10−2 and 10−3 code word error rate, MLLVS codes with as few as 2 passes show an advantage in E_b/N_o when compared to Reed-Solomon codes when used in equivalent concatenated code structures.