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Generalized Spatially-Coupled Product-Like Codes Using Zipper Codes With Irregular Degree

Alvin Y. Sukmadji, Frank R. Kschischang, Mohannad Shehadeh

TL;DR

Simulation results with shortened double-error-correcting Bose-Chaudhuri-Hocquenghem constituent codes show that zipper codes with chevron and half-chevron interleaver maps outperform staircase codes when the rate is below 0.86.

Abstract

Zipper codes with irregular variable degree are studied. Two new interleaver maps -- chevron and half-chevron -- are described. Simulation results with shortened double-error-correcting Bose--Chaudhuri--Hocquenghem constituent codes show that zipper codes with chevron and half-chevron interleaver maps outperform staircase codes when the rate is below 0.86 and 0.91, respectively, at $10^{-8}$ output bit error rate operating point. In the miscorrection-free decoding scheme, both zipper codes with chevron and half-chevron interleaver maps outperform staircase codes. However, constituent decoder miscorrections induce additional performance gaps.

Generalized Spatially-Coupled Product-Like Codes Using Zipper Codes With Irregular Degree

TL;DR

Simulation results with shortened double-error-correcting Bose-Chaudhuri-Hocquenghem constituent codes show that zipper codes with chevron and half-chevron interleaver maps outperform staircase codes when the rate is below 0.86.

Abstract

Zipper codes with irregular variable degree are studied. Two new interleaver maps -- chevron and half-chevron -- are described. Simulation results with shortened double-error-correcting Bose--Chaudhuri--Hocquenghem constituent codes show that zipper codes with chevron and half-chevron interleaver maps outperform staircase codes when the rate is below 0.86 and 0.91, respectively, at output bit error rate operating point. In the miscorrection-free decoding scheme, both zipper codes with chevron and half-chevron interleaver maps outperform staircase codes. However, constituent decoder miscorrections induce additional performance gaps.
Paper Structure (15 sections, 11 equations, 11 figures, 2 tables)

This paper contains 15 sections, 11 equations, 11 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Zipper Codes
  3. Constituent Code, Zipping Pair, and Buffer
  4. Interleaver Map
  5. Encoding and Decoding Procedure
  6. Specific Interleaver Maps
  7. Factor Graph
  8. Regular and Irregular Interleaver Maps
  9. Design Example
  10. Simulation Results
  11. Performance versus Rate Trade-off
  12. Discussion
  13. Encoder Memory Size
  14. BCH Constituent Code Shortening and Miscorrection Rate
  15. Conclusion

Figures (11)

  • Figure 1: Example of a zipper code with $n=14$, $m=7$, $r=3$. The first seven columns belong to the virtual buffer and the last seven columns belong to the real buffer. The virtual and real buffers are demarcated by the thick vertical line. The virtual bit in position $(13,2)$ is a copy of the bit in position $(1,12)$, i.e., $\phi(13,2)=(1,12)$. This figure is modified from Fig. 1 of sukmadji.
  • Figure 2: Factor graph of zipper codes. Here, we have the degree of the real bit vertices (circle) $\deg_b(0,n-m)=4$, $\deg_b(0,n-m+1)=3$, $\deg_b(0,n-1)=2$, and $\deg_b(1,n-m)=3$. The degree of each codeword/row vertex (square) is $n$.
  • Figure 3: Example of a staircase code (in its zipper code format) with $m=4$, $n=2m=8$.
  • Figure 4: Chevron interleaver map with $m'=4$, $m=2m'=8$, and $n=3m'=12$.
  • Figure 5: Half-chevron interleaver map with $m'=2$, $m=3m'=6$, and $n=5m'=10$.
  • ...and 6 more figures

Theorems & Definitions (5)

  • Definition 2.1
  • Definition 2.2
  • example 1: Staircase codes
  • example 2: Chevron interleaver map
  • example 3: Half-chevron interleaver map