Systolic GF(2) solver

src/main/scala/chipsldpc/GaussJordan/ contains a binary processing-element mesh and a framed row-stream solver.

Processing elements and mesh

GjOpcode fixes the two-bit row protocol:

Value	Operation	Column behavior `(data output, next state)`
`00`	`Pass`	`(input, state)`
`01`	`Swap`	`(state, input)`
`10`	`Add`	`(state XOR input, state)`
`11`	`Lock`	`(state, input)`

PeDiag detects and stores pivots. PeCol applies the diagonal opcode to its local bit. Both use active-high synchronous reset and hold registered state when en_i is low.

TrapezoidMeshConfig(n, liftedCols, reduceHopDelay, exposeFullState) creates n rows and n + liftedCols columns. Data moves down, opcodes move right, and the reduce token moves between diagonal cells after reduceHopDelay enabled clocks. Optional state exports are packed row-major. Emitted module names are pe_col, pe_diag, and trapeziod_mesh.

Framed solver

SystolicGf2SolverConfig(width, maxRows) fixes the coefficient width and row capacity. One frame uses four Decoupled channels:

Channel	Direction	Payload
`start`	input	runtime row count and active coefficient columns
`row`	input	one `width`-bit coefficient row and one RHS bit
`solution`	output	logical slot, bit value, and `last`
`result`	output	consistency flag and solver clocks

The solver handles one right-hand side per frame. It reverses active coefficient columns at the mesh boundary because the physical mesh gives the highest column first pivot priority. The public stream remains in ascending logical-slot order. For a consistent rank-deficient system, dependent or free slots are zero in the returned canonical witness.

The internal mesh uses width rows, one lifted RHS column, a reduce-hop delay of three, and no full-state debug export. With a row accepted on every feed clock, a nonempty frame reports

\[\text{rows} + 3\,\text{width} + 1\]

solver clocks. A zero-row frame reports zero. Gaps while rows are supplied add feed clocks. Solution and result backpressure do not change the captured solver count.

Inconsistent frames emit no solution records. Consistent frames with nonzero activeCols emit exactly that many records before the result.

Inspect and test

./scripts/emit.sh pe-col
./scripts/emit.sh pe-diag
./scripts/emit.sh trapezoid-mesh
./mill chipsLDPC.test.testOnly chipsldpc.GaussJordan.GaussJordanPESpec
./mill chipsLDPC.test.testOnly chipsldpc.GaussJordan.TrapezoidMeshSpec
./mill chipsLDPC.test.testOnly chipsldpc.GaussJordan.SystolicGf2SolverSpec

The full solver is also instantiated by Filtered OSD-0.