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

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. We propose a variation of Tanner's construction for quasi-cyclic low-density parity-check codes in a way that allows us to use NON-prime lifting sizes by using some arithmetic sequences instead of geometric sequences. We prove two theorems on the values of this lifting sizes so that the resulting code has girth at least 8. The resulting codes turned out to have better performance in terms of frame error rate at code lengths around 500, which is confirmed by computer simulation. image