(S_\ell^\*,D_\ell^\*) relation

Read the equation

This expression selects a state or parameter setting that minimizes the displayed objective. Its terms describe what is penalized or fitted; the feasible domain, term weights and an actual solver determine the resulting solution.

Terms & definitions

The recovered passage does not supply a separate symbol table. Read the source context for the notation used in this version; familiar letters may carry different meanings in other builds.

How it works

1. Read (S_\ell^\,D_\ell^\) as the quantity being defined or updated by this relation.

2. Applies the stated minimum, maximum, or clamp. These bounds are part of the actual operation.

3. Use this version’s variable definitions and update order. The same symbol may be assigned a different meaning in another build.

Assumptions & limits

Source recovery establishes that the expression appears in this record. Its mathematical validity, implementation behavior, and interpretation must be assessed separately. See the linked source and research notes for the checks available for this version.

Original context

Each layer gets its own full equation:

For layer ℓ:

(S_\ell^\*,D_\ell^\*)=
\arg\min_{S_\ell',D_\ell'}
\Big[
\|D_\ell'(U,\mathcal{E}_{i16})-B_\ell(S_\ell',\mathcal{E}_{i16})\|
+W_\ell\cdot\text{Cost}_\ell
+R_\ell
+R_{D,\ell}
\Big]

Where each layer has its own deterministic cost:

Layer 1 — Physical
\text{Cost}_1 = a_1\cdot BER + b_1\cdot\frac{1}{SNR}

Layer 2 — Link

(S_\ell^\*,D_\ell^\*)=
\arg\min_{S_\ell',D_\ell'}
\Big[
\|D_\ell'(U,\mathcal{E}_{i16})-B_\ell(S_\ell',\mathcal{E}_{i16})\|
+W_\ell\cdot\text{Cost}_\ell
+R_\ell
+R_{D,\ell}
\Big]

Related builds