LDPC Decoder for Photon-Starved Optical Communication

Overview

A soft-input LDPC decoder ASIC targeting the ChipFoundry chipIgnite shuttle (SkyWater 130nm, Caravel harness). The design targets photon-starved free-space optical communication links such as deep-space optical downlinks, underwater optical modems, and quantum key distribution post-processing. By accepting soft log-likelihood ratio (LLR) inputs rather than hard bit decisions, the decoder preserves 2-3 dB of coding gain that would otherwise be lost at extremely low photon counts. The entire decoder fits in approximately 1.5 mm^2 of the Caravel user area with no multipliers -- only adders, comparators, and shift registers.

Application

The target channel is a photon-counting optical link using Geiger-mode avalanche photodiode (GMAPD) detectors, such as the BAE Systems single-photon detector array. At photon-starved signal levels (0.5-5 photons per slot), the receiver produces soft detection statistics governed by Poisson counting noise. Channel LLRs are computed from these statistics by the Caravel PicoRV32 management core and written to the decoder via Wishbone. The rate-1/8 LDPC code provides extreme redundancy (32 information bits encoded into 256 coded bits), enabling reliable communication well below 1 photon per bit -- approaching the theoretical limits of optical communication.

Architecture

Caravel SoC (Sky130, chipIgnite)
+=================================================+
|  PicoRV32 (Management Core)                     |
|      |                                          |
|      | Wishbone B4 bus                          |
|      v                                          |
|  ldpc_decoder_top (~1.5 mm^2)                   |
|    +-- wishbone_interface (register map)         |
|    +-- ldpc_decoder_core (layered min-sum)       |
|    |     +-- llr_ram (256 x 6-bit)               |
|    |     +-- msg_ram (edges x 6-bit)             |
|    |     +-- vn_update_array [Z=32]              |
|    |     +-- cn_update_array [Z=32]              |
|    |     +-- barrel_shifter_z32                  |
|    |     +-- iteration_controller                |
|    |     +-- syndrome_checker                    |
|    +-- hard_decision_out (32 decoded bits)        |
|                                                  |
|  Data flow: LLRs in -> layered decode -> 32 bits |
+=================================================+

The decoder uses layered (row-serial) scheduling of the offset min-sum algorithm. Each layer processes one row of the 7x8 QC-LDPC base matrix, updating variable-node beliefs immediately rather than waiting for a full flooding iteration. This roughly halves the iteration count needed for convergence. A barrel shifter handles the quasi-cyclic shift operations at the Z=32 lifting factor.

The design uses a single clock domain (wb_clk_i from Caravel) and contains no multipliers or lookup tables -- all arithmetic is add/compare/select. This makes it well suited for area-constrained ASIC implementation on Sky130.

Code Parameters

Parameter	Value
Code type	QC-LDPC (quasi-cyclic)
Rate	1/8 (k=32, n=256)
Base matrix	7x8 IRA staircase
Lifting factor Z	32
Quantization	6-bit signed LLR
Algorithm	Offset min-sum (beta ~ 0.5)
Scheduling	Layered (row-serial)
Max iterations	30 (with early termination)
Convergence	~2x faster than flooding schedule

Performance

Metric	Value
Achieved clock	50 MHz (TT/FF corners met, SS fails)
Cycles per codeword	~630 (30 iterations x 21 cycles/iter)
Codeword latency	~12.6 us @ 50 MHz
Decoded throughput	~2.5 Mbps
Cell count	186,444 (post-synthesis)
Die area (macro)	2800 x 1760 um (4.93 mm^2)
Core utilization	30%
Coding gain vs hard	+2-3 dB at BER 10^-5

Register Map

All registers are accessed via Wishbone B4 at word-aligned addresses relative to the decoder base address.

Offset	Name	R/W	Description
0x00	CTRL	R/W	[0]=start, [1]=early_term_en, [12:8]=max_iter
0x04	STATUS	R	[0]=busy, [1]=converged, [12:8]=iter_used, [23:16]=syndrome_wt
0x10-0xDC	LLR_IN	W	52 words: 5 LLRs packed per 32-bit word (6 bits each)
0x50	DECODED	R	32 decoded information bits
0x54	VERSION	R	0x1D010001 (LDPC v1.0, rev 1)

Typical usage from PicoRV32 firmware:

1. Write 256 quantized LLRs to LLR_IN (52 Wishbone writes)
2. Write CTRL to start decode (max_iter=30, early_term=1)
3. Poll STATUS until busy=0
4. Read DECODED bits and syndrome weight

Verification Status

Layer	Status	Details
Standalone Verilator	PASS (2/2)	VERSION register read, clean codeword decode
Vector-driven Verilator	PASS (20/20)	Bit-exact match vs Python behavioral model
cocotb RTL simulation	PASS (5/5)	basic, noisy, max_iter, back_to_back, demo
Gate-level simulation	PASS (5/5)	All 5 tests pass on post-route GL netlist
Static timing analysis	50 MHz MET (TT)	WNS = +3.28 ns (TT), SS corner fails
Precheck	17/19 PASS	KLayout FEOL crash + LVS cosmetic pin-match

The Python behavioral model (model/ldpc_sim.py) generates test vectors at multiple SNR points covering the Poisson channel at lambda_s = 0.5, 1.0, 2.0, and 5.0 photons per slot. All 20 vector-driven tests produce bit-exact agreement between RTL and the Python reference.

Hardening Results

The decoder macro was hardened using OpenLane 2 (LibreLane) targeting SkyWater 130nm. Key results from the successful run (Run 6, balanced_popcount):

Metric	Result
DRC (Magic)	Clean
DRC (KLayout)	Clean
LVS	Clean (macro), cosmetic pin-match at wrapper level
Antenna violations	1,179 (accepted, internal nets only)
Hold violations	0 reg-to-reg (input port violations fixed via SDC)
Setup WNS (TT nom)	+3.28 ns
Setup WNS (FF min)	+6.53 ns

See docs/hardening-results.md for full multi-corner timing data across all 7 runs.

Directory Structure

chip_ignite/
  verilog/
    rtl/                  RTL sources (decoder + Caravel wrapper)
      ldpc_decoder_top.sv     Top-level with Wishbone interface
      ldpc_decoder_core.sv    Layered min-sum decode engine
      wishbone_interface.sv   Register map and bus logic
      user_project_wrapper.v  Caravel integration wrapper
    dv/
      cocotb/ldpc_tests/  cocotb testbenches for Caravel sim
    gl/                   Gate-level netlists (post-hardening)
    includes/             File lists for simulation
  openlane/
    ldpc_decoder_top/     OpenLane config, SDC, pin ordering
    user_project_wrapper/ Wrapper hardening config
  firmware/
    ldpc_demo/            PicoRV32 bare-metal demo firmware
  docs/                   Sphinx documentation, AI disclosure
  gds/                    GDSII output (post-hardening)
  lef/                    LEF macro definitions
  sdc/                    Timing constraints

The parent directory (ldpc_optical/) contains additional resources:

• rtl/ -- standalone RTL (pre-integration)
• tb/ -- Verilator testbenches with vector-driven tests
• model/ -- Python behavioral model and test vector generation
• data/ -- H-matrix definitions and simulation results
• docs/ -- Design documentation and project report

Building and Running

Standalone RTL verification (Verilator)

# Basic functional tests (VERSION read + clean decode)
cd ../tb && make sim

# 20-vector cross-check against Python behavioral model
cd ../tb && make sim_vectors

Caravel flow (requires ChipFoundry CLI)

# One-time setup
cf init
cf setup

# Harden the decoder macro
cf harden ldpc_decoder_top

# Integrate into Caravel wrapper
cf harden user_project_wrapper

# Configure GPIO pins
cf gpio-config

# Run cocotb verification (RTL)
cf verify ldpc_basic

# Run gate-level simulation
cf verify ldpc_basic --sim gl

# Shuttle compliance precheck
cf precheck

Python behavioral model

cd ../model
python3 ldpc_sim.py

Roadmap

Current (Approach A -- Minimal Viable Submission): Wishbone-attached decoder verified in simulation. PicoRV32 firmware injects test LLRs, decodes, and reports results over UART. No external optical hardware required for the demo.

Future (Approach B -- Full Optical Frontend): Populated PCBA with SiPM or GMAPD detector, transimpedance amplifier (AD8015), and fast comparator. External RP2040 MCU computes real-time LLRs from photon counts. Bench-scale free-space optical link demo (1-5 m).

Future (Approach C -- Silicon Return): After chipIgnite silicon returns (Oct/Nov 2026): build full reference board, demonstrate free-space optical link with BAE Systems GMAPD detector, and characterize real-silicon BER performance against simulation predictions. Target applications include CubeSat optical downlinks and underwater optical modems.

License

Licensed under the Apache License, Version 2.0. See LICENSE for the full text.

AI Disclosure

Portions of this project were developed with AI assistance. See docs/ai-disclosure.md for details.