Some variations of Tanner's construction for short length QC‐LDPC codes

Abstract

Abstract This paper proposes a modification to Tanner's work for constructing girth‐8 quasi‐cyclic low‐density parity‐check codes. The main contribution of this paper is to use an arithmetic sequence at the leftmost column for the exponent matrix so that the lifting size is not necessarily restricted to the prime numbers. Two theorems on the lifting sizes that achieve girth at least 8 using this approach is also provided. This construction exhibits better frame error rate results to the modified 5G new radio (NR) low‐density parity‐check codes for lengths around 500. Also, this construction achieves better frame error rate performance results than the recently proposed one using the Golomb rulers at around frame error rate of 10−6.

Keywords

• channel coding
• error‐correction codes
• linear codes
• parity‐check codes