Zipper Codes

TL;DR

Stall patterns that can arise in iterative decoding are analyzed, giving a means of error floor estimation in zipper codes.

Abstract

Zipper codes are a framework for describing spatially-coupled product-like codes. Many well-known codes, such as staircase codes and braided block codes, are subsumed into this framework. New types of codes such as tiled diagonal and delayed diagonal zipper codes are introduced along with their software simulation results. Stall patterns that can arise in iterative decoding are analyzed, giving a means of error floor estimation.

Figures (14)

• Figure 1: Example of a zipper code with a systematically encoded $\mathcal{C}_i=\mathcal{C}$ constituent code with $n=n_i=14$ and $r=r_i=3$. Tiles in the shaded region represent virtual symbols, while tiles in the unshaded and filled regions represent real symbols. The filled regions show the location of parity symbols. The two tiles connected by arrows represent the two coordinates prescribed by the interleaver map. In this example, we have $\phi(13,2)=(1,12)$ and $c_{13,2}=c_{1,12}=1$. Each row is a codeword of $\mathcal{C}$. Rows with lower row indices correspond to "older" rows while those with higher indices are regarded as "newer." The icons next to "Virtual" and "Real" at the top of the figure correspond to the shape of the virtual and real buffers in the first 14 rows. The virtual and real buffers are demarcated by a bold line.
• Figure 2: Staircase code (left); corresponding zipper code (right).
• Figure 3: Tightly braided code with $(7,4)$ Hamming constituent code (left); corresponding zipper code (right), with numbers indexing constituent codewords.
• Figure 4: Tiled diagonal zipper code with $L=3$, tile size $w\times w$, and interleaver map as described in \ref{['eq:phitileddiagonal']}.
• Figure 5: Delayed diagonal zipper code with $m=8$ and various delay values $\delta$.

Theorems & Definitions (9)

• Definition 1
• Definition 2
• example 1
• example 2
• Theorem 1
• Proposition 1
• Theorem 2
• Proposition 2
• example 3