Flip CRC modification for message length detection

Abstract

Cyclic redundancy check (CRC) bits that are conventionally used for error detection have recently found a new application in universal mobile telecommunications system standard for message length detection of variable-length message communications. It was anticipated that the CRC bits, when they are coworked with the inner convolutional code, can be used to detect the receiver-unaware of the message length-without much degradation in their error detection capability. This is unfortunately not true when the offset or difference between the wrong detected length and the true length is small. Two improvements, i.e., the DoCoMo's reverse CRC method and the flip CRC method, were accordingly proposed. In this paper, we revisited the flip CRC modification by considering the impact of joint decoding of the CRC code and the convolutional code. By generalizing the condition for the selection of the flip polynomials, we found that under error-free transmission, the range of the length offsets, at which the false length probability conditioning on the true message length can be made exactly zero (and hence, is minimized), can be extended from l - 1 to l + m - 1, where f and m are, respectively, the number of the CRC bits and the memory order of the convolutional code. In addition, an upper bound and a lower bound for the overall false length probability with respect to a uniform pick of the true message length over a candidate message length set are derived. It is then confirmed numerically that the two bounds almost coincide for moderate (f + m) value. Simulations show that the false length probability obtained analytically under error-free transmission assumption only mildly degrades for moderate-to-high SNRs. Interestingly, we also found that the system block error rate of the flip CRC method can be well approximated by the performance curve of the adopted convolutional code up to a certain SNR, and approach an error floor determined well by the previously derived false length probability bounds beyond this SNR, thereby facilitating the selection of the system parameters, such as the number of CRC bits and the memory order of the convolutional code.