Rate-Compatible Tail-Biting Convolutional Codes for M2M Communications

We propose an algorithm to construct a group of rate-compatible tail-biting convolutional codes (RC-TBCCs) with consistently good frame error rate performance for both short and long information lengths. The algorithm considers the free distance property and the minimum distance profile of a TBCC jointly. We construct a group of RC-TBCCs with code rates $1/n$ , $3\leq n\leq 12$ . Numerical results show that the constructed RC-TBCCs have better frame error rate performance than the TBCCs used in LTE standards for various information lengths and code rates.