TY - JOUR
T1 - Optimized Design of Finite-Length Separable Circulant-Based Spatially-Coupled Codes
T2 - An Absorbing Set-Based Analysis
AU - Amiri, Behzad
AU - Reisizadehmobarakeh, Amirhossein
AU - Esfahanizadeh, Homa
AU - Kliewer, Jorg
AU - Dolecek, Lara
N1 - Publisher Copyright:
© 1972-2012 IEEE.
PY - 2016/10
Y1 - 2016/10
N2 - In this paper, we characterize the finite-length performance of separable circulant-based spatially-coupled (SCB-SC) LDPC codes for transmission over the additive white Gaussian noise channel. For a general class of finite-length graph-based codes, it is known that the existence of small absorbing sets causes a performance degradation in the error floor regime. We first present the mathematical conditions for the existence of absorbing sets in binary SCB-SC codes. This analysis enables us to find the exact number of absorbing sets as a function of the design parameters. In particular, our results show that the choice of the cutting vector affects the number of absorbing sets and, therefore, the error floor performance of the code. For a fixed column weight, we find provably optimal cutting vectors that result in the least number of absorbing sets. Furthermore, we extend our analysis to nonbinary SCB-SC codes, where we show that the choice of the cutting vector is not as critical as in the binary case. We provide an algorithm which provably removes the problematic nonbinary absorbing sets from nonbinary SCB-SC codes by informed selection of edge labels. Our simulation results show the superior error floor performance of our designed binary and nonbinary SCB-SC codes compared with binary unstructured and nonbinary quasi-cyclic SC codes available in the open literature.
AB - In this paper, we characterize the finite-length performance of separable circulant-based spatially-coupled (SCB-SC) LDPC codes for transmission over the additive white Gaussian noise channel. For a general class of finite-length graph-based codes, it is known that the existence of small absorbing sets causes a performance degradation in the error floor regime. We first present the mathematical conditions for the existence of absorbing sets in binary SCB-SC codes. This analysis enables us to find the exact number of absorbing sets as a function of the design parameters. In particular, our results show that the choice of the cutting vector affects the number of absorbing sets and, therefore, the error floor performance of the code. For a fixed column weight, we find provably optimal cutting vectors that result in the least number of absorbing sets. Furthermore, we extend our analysis to nonbinary SCB-SC codes, where we show that the choice of the cutting vector is not as critical as in the binary case. We provide an algorithm which provably removes the problematic nonbinary absorbing sets from nonbinary SCB-SC codes by informed selection of edge labels. Our simulation results show the superior error floor performance of our designed binary and nonbinary SCB-SC codes compared with binary unstructured and nonbinary quasi-cyclic SC codes available in the open literature.
KW - Spatially-coupled codes
KW - absorbing sets
KW - array-based codes
KW - error floor performance
KW - finite block length
KW - separable circulant-based
UR - http://www.scopus.com/inward/record.url?scp=84992361714&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84992361714&partnerID=8YFLogxK
U2 - 10.1109/TCOMM.2016.2597287
DO - 10.1109/TCOMM.2016.2597287
M3 - Article
AN - SCOPUS:84992361714
SN - 0090-6778
VL - 64
SP - 4029
EP - 4043
JO - IEEE Transactions on Communications
JF - IEEE Transactions on Communications
IS - 10
M1 - 7529198
ER -