Constituent automorphism decoding of Reed-Muller codes

Abstract

Automorphism-ensemble decoding is applied to the Plotkin constituents of Reed-Muller codes, resulting in a new soft-decision decoding algorithm with state-of-the-art performance versus complexity trade-offs.

Figures (8)

• Figure 1: Illustrated is $\mathbb{T}_{2,4}$. The label of each vertex is $(r,m)$, for some $r\in \mathbb{Z}$ and $m \in \mathbb{Z}^{\geq 0}$, where for brevity the parentheses are omitted. The circled vertices form $\mathbb{T}_{2,4}^{\mathcal{A}^{\ast}}$, the GMC decoding tree for $\mathop{\mathrm{RM}}\nolimits(2,4)$ with atom set $\mathcal{A}^{\ast}$ in (\ref{['eq:atomset']}).
• Figure 2: The address of each vertex in $\mathbb{T}_{3,6}^{\mathcal{A}^{\ast}}$ is indicated below that vertex; the vertex label is indicated above.
• Figure 3: The general architecture of an AE decoder corresponding to an automorphism ensemble of size $\ell$.
• Figure 4: Selection networks with parameters: (a) (4,8), (b) (6,8). Vertical segments denote comparators (having two output ports) and minselectors (having one output port), with an arrow pointing towards the output port corresponding to the minimum input.
• Figure 5: An extensive test of CA decoders of RM$(4,9)$ at BLER=$10^{-3}$. Candidates nodes are those with address in the set $\{ \varnothing, 1, 11, 110, 1100 \}$ with ensemble size for each candidate node ranging from $1$ to $4$.