Channel coding is commonly used to increase the robustness of a digital communication system. The principle underlying channel coding is to introduce redundancy into the transmitted bit stream so as to facilitate error detection and correction at the decoder. One general class of channel codes is trellis codes, and a commonly-used class of trellis codes is known as convolutional codes. Convolutional codes are used extensively in numerous applications in order to achieve reliable data transfer, including digital video, radio, mobile communication, and satellite communication.
According to a mobile communication standard, such as the 3rd Generation Partnership Project (3GPP) specification for Long Term Evolution (LTE), the Physical Downlink Control Channel (PDCCH) is encoded by a rate 1/3 tail biting convolutional code (TBCC), followed by a rate matching unit that produces the final coding rate ranging from 0.04 to 0.99. The rate is defined as m/n, where each m-bit information symbol to be encoded is transformed into an n-bit symbol. Due to this requirement, the user equipment needs to have a TBCC decoder that can perform PDCCH decoding across all supported code rates. This requirement is challenging since the decoder needs to address at least the following three criteria: (i) reasonably good decoding performance; (ii) acceptable decoding complexity for all code rates; and (iii) required timing budget per the 3GPP for all code rates. These criteria are particularly difficult to achieve for the decoding of high code rate TBCC, e.g., having a code rate of 71/72. A convolutional decoder is needed which has acceptable decoding complexity and is within the required timing budget per 3GPP for all code rates, but without sacrificing decoding performance.