Detection Analysis of CRC-Assisted Decoding

Cyclic redundancy check (CRC) codes are used for error detection in many communication systems. Attempts to take advantage of the CRC bits to also improve the error correction performance have been made. In this work, the concurrent use of CRC codes in both error detection and error correction is investigated. The Hamming weight enumerator of the LTE CRC code is found to analyze its undetected error probability (UEP) and its false alarm probability (FAP). Theoretical bounds on the UEP and FAP with concurrent error detection and correction are derived. For theoretical analysis, a hypothetical sphere decoder is assumed, from which insights and recommendations for practical implementations are made.