Optimized Design of Finite-Length Separable Circulant-Based Spatially-Coupled Codes: An Absorbing Set-Based Analysis

Behzad Amiri, Amirhossein Reisizadehmobarakeh, Homa Esfahanizadeh, Jorg Kliewer, Lara Dolecek

Research output: Contribution to journalArticlepeer-review

16 Scopus citations

Abstract

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.

Original languageEnglish (US)
Article number7529198
Pages (from-to)4029-4043
Number of pages15
JournalIEEE Transactions on Communications
Volume64
Issue number10
DOIs
StatePublished - Oct 2016

All Science Journal Classification (ASJC) codes

  • Electrical and Electronic Engineering

Keywords

  • Spatially-coupled codes
  • absorbing sets
  • array-based codes
  • error floor performance
  • finite block length
  • separable circulant-based

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