DPCCC-Toolkit

A complete open-source toolkit for the design and simulation of Decomposed Parallel Concatenated Convolutional Codes (DPCCC), a novel turbo code architecture that significantly increases the minimum Hamming distance (mHD) and reduces the error floor compared to conventional turbo codes such as LTE.

Code: https://github.com/bazzal99/DPCCC-Toolkit

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Paper

M. Bazzal, J. Nadal, S. Weithoffer, C. A. Nour and C. Douillard, "A Novel Parallel Concatenated Convolutional Code Structure Based on Frame Decomposition," 2025 13th International Symposium on Topics in Coding (ISTC), Los Angeles, CA, USA, 2025, pp. 1–5. DOI: 10.1109/ISTC65386.2025.11154568 Preprint: hal-05168399

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What is a DPCCC?

A DPCCC encodes a K-bit information block d₁ through:

1. Encoder C₁ (tail-biting RSC, length K) → first parity stream of length K

2. L independent encoders C₂…C_{L+1} (tail-biting RSC, each length K/L), each receiving an interleaved sub-frame d'_q formed by selecting every L-th bit of d₁ according to the rule:

   d'_q[ℓ] = d₁[ℓ·L + q − 2],   ∀ ℓ < K/L − 1,   q ∈ [2, L+1]
   

The overall code rate is 1/3 (K systematic + K first parity + K total sub-block parity), matching conventional turbo codes while achieving significantly higher mHD.

DPCCC Structure

Key idea: suppressing low-IW TRTZ sequences

In conventional TCs the number of IW-2 TRTZ sequences grows quadratically with K (K·⌊K/p⌋ sequences for period p). DPCCC mitigates this by decomposing the frame: when L mod p ≠ 0, IW-2 single-layer TRTZ sequences are reduced to K·⌊K/lcm(p,L)⌋, and IW-2/IW-3 multi-layer sequences are converted into high-weight TRTZml-w1 sequences.

TRTZ Sequence Decomposition

The three cases from the paper:

• (a) IW-2 → splits into two IW-1 sub-frame sequences → high output weight → mitigated
• (b) IW-3 → similar split, depends on interleaver for suppression → mitigated by design
• (c) IW-4 → both sub-frames carry IW-2 RTZ sequences → must be broken by Π

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mHD Results

Estimated mHD vs LTE TC (from Table I of the paper)

Configuration: Algorithm 1, code rate R = 1/3, G1 = G(1, 15/13)₈, G2 = G(1, 15/13, 17/13)₈ with systematic puncturing pattern [10100000] and parity patterns [11101111] / [01011010].

Config	K=128 G1/G2	K=1024 G1/G2	K=6144 G1/G2
DPCCC L=2	28 / 32	46 / 48	50 / 48
DPCCC L=4	26 / 31	46 / 56	51 / 60
DPCCC L=8	24 / 30	45 / 54	57 / 72
DPCCC L=16	18 / 19	42 / 47	54 / 64
LTE TC	16	26	27

Best gains over LTE: +75% (K=128), +70% (K=1024), +119% (K=6144) using G1, and +100%, +107%, +157% using G2.

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Repository structure

DPCCC-Toolkit/
├── shared/                         ← Shared code used by all three tools
│   ├── config.h                    ← ALL tunable parameters (edit this first)
│   ├── encoder.h / encoder.c       ← Multi-segment tail-biting RSC encoder
│   ├── interleaver.h / interleaver.c  ← ARP interleaver + repetition mapping
│   ├── decoder.h / decoder.c       ← Log-MAP (BCJR) decoder
│   └── utils.h / utils.c           ← Binary ops, AWGN, sorting, file I/O
│
├── interleaver_design/
│   ├── decoder_free/               ← Tool 1: decoder-free mHD design (Algorithm 1)
│   │   ├── include/
│   │   │   ├── design_config.h     ← Threshold, RTZ search depth
│   │   │   ├── rtz_search.h        ← DPCCC-aware RTZ graph-girth kernel
│   │   │   └── designer.h          ← Layer-by-layer ARP design
│   │   ├── src/
│   │   │   ├── main.c
│   │   │   ├── designer.c
│   │   │   └── rtz_search.c
│   │   └── Makefile
│   │
│   └── double_impulse/             ← Tool 2: N-impulse decoder-based design (DIM/EVIM)
│       ├── include/
│       │   ├── design_config.h     ← IMPULSE_N (1/2/3), threshold, SNR
│       │   └── designer.h          ← Threaded impulse method
│       ├── src/
│       │   ├── main.c
│       │   └── designer.c
│       └── Makefile
│
├── montecarlo/                     ← Tool 3: BER/FER Monte Carlo simulator
│   ├── include/sim_config.h        ← RNG seed, target frame errors
│   ├── src/main.c
│   └── Makefile
│
└── docs/figures/                   ← Paper figures (SVG)
    ├── dpccc_structure.svg
    ├── trtz_sequences.svg
    └── mhd_table.svg

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Configuration

All shared parameters are in shared/config.h. The most important ones:

#define SIZE      1024   /* Information block length K                      */
#define CUTS      2      /* Number of decompositions L (parity sub-blocks)  */
#define ARP_Q     4      /* ARP sub-interleaver period Q                    */
#define DELAYS    3      /* RSC memory elements (2^DELAYS trellis states)   */
#define G1_INIT   {1,1,0,1}   /* RSC feedforward polynomial G1             */
#define G2_INIT   {1,0,1,1}   /* RSC feedback polynomial G2                */
#define ENCODER_PERIOD  7     /* RSC impulse response period (7 for LTE)   */

Selecting L (number of decompositions)

The paper provides clear guidance (Section IV-C):

• L mod p ≠ 0 is required (do not use L that is a multiple of the encoder period p=7)
• Small L is preferred for short frames; larger L benefits large frames
• Recommended values from Table I: L=2 for K≤1024, L=8 for K=6144

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Tool 1: Decoder-free interleaver design (Algorithm 1 from paper)

Implements the iterative coordinate-descent design of Section IV-E, using the decoder-free RTZ graph-girth search from [7] as the distance oracle. Each sub-interleaver Πq is designed sequentially, conditioned on all previously designed interleavers Π₂…Π_{q-1}.

cd interleaver_design/decoder_free
# Edit include/design_config.h: set DESIGN_THRESHOLD, IWM_MAX_WEIGHT, etc.
make
./dpccc_decoder_free

Output (result.txt) — C-initialiser format:

int total_S[2][4] = { {1, 3, 7, 2}, {0, 5, 4, 1} };
int total_P[2]    = {11, 7};
distance = 46

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Tool 2: N-impulse interleaver design (DIM / EVIM variant)

Evaluates ARP candidates by injecting N simultaneous high-LLR impulses into the turbo decoder (N=1: SIM, N=2: DIM, N=3: triple). Set IMPULSE_N in include/design_config.h. Parallelised across all CPU cores via pthreads.

cd interleaver_design/double_impulse
# Edit include/design_config.h: set IMPULSE_N (1/2/3), DESIGN_THRESHOLD, IMPULSE_SNR
make
./dpccc_impulse

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Tool 3: Monte Carlo BER/FER simulator

Simulates BER and FER over AWGN using log-MAP decoding with MAX_ITERATIONS turbo iterations. The interleaver is loaded from ARP_SEMI_Initialization() in shared/interleaver.c — update the hardcoded S[], P arrays there with your designed interleaver.

cd montecarlo
# Edit shared/config.h: SNR_MIN, SNR_MAX, SNR_STEP, MAX_ITERATIONS
# Edit shared/interleaver.c: update ARP_SEMI_Initialization() with your S, P
make
./dpccc_sim

Output (result.txt):

SNR = 2.00
BER = [1.2340000e-02, 3.4560000e-03, ...]
FER = [4.5670000e-02, 1.2340000e-02, ...]

Performance note: The simulator is single-threaded. For large K or high SNR (deep waterfall / error floor), parallelise Build_SNR() with pthreads — the loop structure is already designed for it.

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Building

Each tool builds independently:

# Tool 1
cd interleaver_design/decoder_free && make

# Tool 2
cd interleaver_design/double_impulse && make   # requires pthreads

# Tool 3
cd montecarlo && make

Requires: GCC with C99 support, libm. Tool 2 additionally requires -lpthread.

Clean all:

make clean   # run inside each tool directory

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RSC encoder notes

Two encoder configurations are used in the paper:

Name	Generator	Puncturing	Notes
G1	G(1, 15/13)₈	none	Single-parity RSC
G2	G(1, 15/13, 17/13)₈	data: [10100000], parity₁: [11101111], parity₂: [01011010]	Double-parity RSC with systematic puncturing

Set in shared/config.h via G1_INIT, G2_INIT, and the PUNCT_* defines.

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License

MIT License. See LICENSE.
Copyright © 2025 Mohammad Bazzal, IMT Atlantique, Lab-STICC, Brest, France.

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Citation

@inproceedings{bazzal2025dpccc,
  author    = {Bazzal, Mohammad and Nadal, J{\'e}r{\'e}my and Weithoffer, Stefan
               and {Abdel Nour}, Charbel and Douillard, Catherine},
  title     = {A Novel Parallel Concatenated Convolutional Code Structure
               Based on Frame Decomposition},
  booktitle = {2025 13th International Symposium on Topics in Coding (ISTC)},
  address   = {Los Angeles, CA, USA},
  pages     = {1--5},
  year      = {2025},
  doi       = {10.1109/ISTC65386.2025.11154568}
}

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Related repository

The decoder-free mHD estimation method used by Tool 1 is also available as a standalone tool for LTE turbo codes:

Decoder-Free-Turbo-mHD_Estimator