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International Journal of Speech Technology

Performance analysis of short length low density parity check codes

Anand Anbalagan, Sivakannan Subramani, C. Kamalanathan, Sunita Panda

Published Apr 8, 2021• 1 citation
Publisher
DOI
10.1007/s10772-021-09815-1

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Low-Density-Parity-Check-Codes taken as a kind of advanced channel coding mode,have become the powerful competitor of the fourth generation of communication system.The LDPC advanced by Gallager has standard Tanner figure structure,and the advantage of the performance can be materialized after the length of the codes become longer.When the length is short or of medium sized,the performance of coding will fall down in a way because of the existence of short girth in the Tanner figure.With the improvement of structure method advanced by Gallager,the short girth in which length is 4 can be eliminated,thus the performance of coding can be raised.
A generalized low-density parity check code (GLDPC) is a low-density parity check code in which the constraint nodes of the code graph are block codes, rather than single parity checks. In this paper, we study GLDPC codes which have BCH or Reed-Solomon codes as subcodes under bounded distance decoding (BDD). The performance of the proposed scheme is investigated in the limit case of an infinite length (cycle free) code used over a binary erasure channel (BEC) and the corresponding thresholds for iterative decoding are derived. The performance of the proposed scheme for finite code lengths over a BEC is investigated as well. Structures responsible for decoding failures are defined and a theoretical analysis over the ensemble of GLDPC codes which yields exact bit and block error rates of the ensemble average is derived. Unfortunately this study shows that GLDPC codes do not compare favorably with their LDPC counterpart over the BEC. Fortunately, it is also shown that under certain conditions, objects identified in the analysis of GLDPC codes over a BEC and the corresponding theoretical results remain useful to derive tight lower bounds on the performance of GLDPC codes over a binary symmetric channel (BSC). Simulation results show that the proposed method yields competitive performance with a good decoding complexity trade-off for the BSC.