# Low-Complexity Lossless Coding of Asynchronous Event Sequences for Low-Power Chip Integration

^{*}

## Abstract

**:**

## 1. Introduction

**(1)**- A novel low-complexity lossless compression method for encoding raw event data represented as asynchronous event sequences, which is suitable for hardware implementation into ESP chips.
**(2)**- A novel low-complexity coding scheme for encoding residual errors by dividing the input range into several coding ranges arranged at concentric distances from an initial prediction.
**(3)**- A novel event sequence representation that removes the event timestamp information by dividing the input sequence into ordered same-timestamp event subsequences that can be encoded in separated bit streams.
**(4)**- A lossless event data codec that provides random access (RA) to any time window by using additional header information.

## 2. State-of-the-Art Methods

## 3. Proposed Low-Complexity Lossless Coding Framework

- spatial information $({x}_{i},{y}_{i}),\forall {x}_{i}\in [1,\phantom{\rule{0.166667em}{0ex}}H],{y}_{i}\in [1,\phantom{\rule{0.166667em}{0ex}}W],$ i.e., the pixel positions where the event was triggered;
- polarity information ${p}_{i}\in \{-1,\phantom{\rule{0.166667em}{0ex}}1\},$ where the symbol “$-1$” signals a decrease and symbol “1” signals an increase in the light intensity; and
- timestamp ${t}_{i},$ the time when the event was triggered.

#### 3.1. Proposed Sequence Representation

#### 3.2. Proposed Triple Threshold-Based Range Partition (TTP)

- (c1)
- ${b}_{0}$ is set by checking $\left|\u03f5\right|<\Delta .$ If true then ${b}_{0}=0;$ otherwise, ${b}_{0}=1.$
- (c2)
- If ${b}_{0}=0,$ then ${b}_{1}$ is set by checking $\left|\u03f5\right|<{\delta}_{1}.$ If true, then ${b}_{1}=0$ and R1 is employed to represent $\u03f5$ on ${n}_{\u03f5}={n}_{{\delta}_{1}}+1$ bits; otherwise ${b}_{1}=1.$
- (c3)
- If ${b}_{1}=1,$ then ${b}_{2}$ is set by checking $\left|\u03f5\right|<{\delta}_{1}+{\delta}_{2}.$ If true then ${b}_{2}=0$ and R2 is employed to represent $\u03f5$ on ${n}_{\u03f5}={n}_{{\delta}_{2}}+1$ bits. Otherwise, ${b}_{1}=1$ and R3 is used to represent $\u03f5$ on ${n}_{\u03f5}={n}_{{\delta}_{3}}+1$ bits.
- (c4)
- If ${b}_{0}=1,$ then ${b}_{1}$ is set by checking $x\le {x}_{1}.$ If true, then ${b}_{1}=0$ and R4 is employed to represent $x-1$ on ${n}_{1}$ bits. Otherwise, ${b}_{1}=1$ and R5 is used to represent $H-x$ on ${n}_{2}$ bits.

Algorithm 1: Encode a general x by using TTP |

Algorithm 2: Decode a general x by using TTP |

#### 3.2.1. Deterministic Cases

#### 3.2.2. Algorithm Variations

#### 3.3. Proposed Method

Algorithm 3: Encode the subsequence of ordered events |

**(i)**- Encode ${N}_{e}^{k}$ by employing TTP${}_{e}$ using ${\widehat{N}}_{e}^{k},$ computed by (1), and ${\mathbf{\Delta}}_{e}$;
**(ii)**- Encode ${e}_{1}^{k}$ as follows:
**(ii.1)**- ${y}_{1}^{k}$ by employing TTP${}_{x}$ using ${\widehat{y}}_{r}^{k}$ computed by (2), range $[1,\phantom{\rule{0.166667em}{0ex}}W],$ and ${\mathbf{\Delta}}^{e1};$
**(ii.2)**- ${x}_{1}^{k}$ by employing TTP${}_{x}$ using ${\widehat{x}}_{r}^{k}$ computed by (2), range $[1,\phantom{\rule{0.166667em}{0ex}}H],$ and ${\mathbf{\Delta}}^{e1};$ and
**(ii.3)**- ${p}_{1}^{k}$ using binarization;

**(iii)**- The remaining events are encoded as follows:
**(iii.1)**- ${y}_{i}^{k}$ by employing TTP${}_{y}$ using ${\widehat{y}}_{i}^{k}={y}_{i-1}^{k},$ range $[{\widehat{y}}_{i}^{k},\phantom{\rule{0.166667em}{0ex}}W],$ and ${\mathbf{\Delta}}_{W}^{k};$
**(iii.2)**- ${x}_{i}^{k}$ by employing TTP${}_{x}$ using ${\widehat{x}}_{i}^{k}$ computed by (3), ${\u03f5}_{{y}_{i}^{k}},$ range $[1,\phantom{\rule{0.166667em}{0ex}}H],$ and ${\mathbf{\Delta}}_{H}^{k};$ and
**(iii.3)**- ${p}_{i}^{k}$ using binarization.

**(iv)**- Update the triple thresholds ${\mathbf{\Delta}}_{H}^{k}$ and ${\mathbf{\Delta}}_{W}^{k}.$

#### 3.3.1. Prediction

#### 3.3.2. Threshold Setting

#### 3.3.3. Random Access Functionality

#### 3.3.4. A Coding Example

## 4. Experimental Evaluation

#### 4.1. Experimental Setup

- (c1)
- Compression ratio (CR), defined as the ratio between the raw data size and the compressed file size;
- (c2)
- Relative compression (RC), defined as the ratio between the compressed file size of a target codec and the compressed file size of LLC-ARES; and
- (c3)
- Bit rate (BR), defined as the ratio between the compressed file size in bits and the number of events in the asynchronous event sequence, measured in bits per event (bpev), e.g., raw data has 64 bpev.

- (t1)
- Event density (${\rho}_{E}$), defined as the ratio between the number of events in the asynchronous event sequence and the encoding/acquisition time, measured in millions of events per second (Mevps);
- (t2)
- Time ratio (TR), defined as the ratio between the data acquisition time and the codec encoding time; and
- (t3)
- Runtime, defined as the ratio between the encoding/decoding time ($\mathsf{\mu}$s) and the number of events.

#### 4.2. Compression Results

- (i)
- an average CR improvement of $5.49\%$, $11.45\%$, and $35.57\%,$ respectively;
- (ii)
- an average BR improvement of $7.37\%,$ $13.40\%,$ and $37.12\%,$ respectively; and
- (iii)
- an average bitsavings of $1.09$ bpev, $1.99$ bpev, and $5.50$ bpev, respectively.

#### 4.3. Runtime Results

**(i)**- an average event density improvement of $234\times $, $412\times ,$ and $2086\times ,$ respectively; and
**(ii)**- an average TR improvement of $216\times ,$ $401\times ,$ and $1969\times ,$ respectively.

#### 4.4. RA Results

## 5. Conclusions

- (1)
- an average CR improvement of $5.49\%$, $11.45\%$, and $35.57\%;$
- (2)
- an average BR improvement of $7.37\%,$ $13.40\%,$ and $37.12\%;$
- (3)
- an average bitsavings of $1.09$ bpev, $1.99$ bpev, and $5.50$ bpev;
- (4)
- an average event density improvement of $234\times $, $412\times ,$ and $2086\times ;$ and
- (5)
- an average TR improvement of $216\times ,$ $401\times ,$ and $1969\times $.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

DVS | Dynamic Vision Sensor |

APS | Active Pixel Sensor |

DAVIS | Dynamic and Active-pixel VIsion Sensor |

EF | Event Frame |

RA | Random Access |

TALVEN | Time Aggregation-based Lossless Video Encoding for Neuromorphic sensor |

ESP | Event Signal Processing |

SoC | System-on-a-chip |

EMI | Event Map Image |

CPV | Concatenated Polarity Vector |

HEVC | High Efficiency Video Coding |

SNN | Spike Neural Network |

EGC | Elias-Gamma-Coding |

LLC-ARES | Low-Complexity Lossless AsynchRonous Event Sequences |

LLC-ARES-RA | LLC-ARES with RA |

ZLIB | Zeta Library |

LZMA | Lempel–Ziv–Markov chain Algorithm |

G-PCC | Geometry-based Point Cloud Compression |

CR | Compression Ratio |

BR | Bitrate |

TR | Time Ratio |

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**Figure 1.**The proposed low-complexity lossless coding framework. The input asynchronous event sequence, ${\mathcal{S}}_{\mathcal{T}},$ is first represented by using the proposed event representation as a set of same-timestamp subsequences, ${\mathcal{S}}^{k},$ having same-timestamp ${t}^{k},$ and then encoded losslessly by employing the proposed method. The output bitstream of each same-timestamp subsequence can be stored in memory as a compressed file. Moreover, it can also be collected as a package bitstream for all the timestamps found in a time period ${\Delta}_{RA}$ and then stored in memory together with bitstream-length information stored as a header as a compressed file with RA, so that the proposed codec can provide RA to any time window of size ${\Delta}_{RA}$.

**Figure 2.**The proposed representation based the proposed same-timestamp (ST) order (on the right) in comparison with the sensor’s event-by-event (EE) order (on the left). The red arrow shows the write-to-file order used to generate the input data files feed to the traditional methods.

**Figure 3.**The proposed low-complexity coding scheme, triple threshold-based range partition (TTP). (

**a**) TTP range partition. (

**b**) TTP decision tree. (

**c**) TTP${}_{y}$ range partition. (

**d**) TTP${}_{y}$ decision tree. (

**e**) TTP${}_{e}$ range partition. (

**f**) TTP${}_{e}$ decision tree. (

**g**) TTP${}_{L}$ range partition. (

**h**) TTP${}_{L}$ range partition.

**Figure 4.**Deterministic cases: (

**a**) if ${x}_{1}<1$ or ${x}_{2}>H,$ then condition (c4) is not checked when building the context tree and one bit is saved. (

**b**) If $x\in ({x}_{1}-{2}^{{n}_{1}-1},\phantom{\rule{0.166667em}{0ex}}{2}^{{n}_{1}-1}]$, then x is represented by using one bit less than in the case when $x\in [1,\phantom{\rule{0.166667em}{0ex}}{x}_{1}-{2}^{{n}_{1}-1}]$ or $x\in ({2}^{{n}_{1}-1},\phantom{\rule{0.166667em}{0ex}}{x}_{1}]$.

**Figure 5.**The encoding workflow using the proposed LLC-ARES method as an asynchronous event sequence of $2\phantom{\rule{0.166667em}{0ex}}\mathsf{\mu}$s time-length, containing 23 events. The input sequence, represented by using the EE order, is first grouped and rearranged by using the proposed ST order. LLC-ARES encodes each data structure by using different TTP variations as an output bitstream of 316 bits stored by using 40 bytes, i.e., 40 numbers having an 8-bit representation.

**Figure 6.**(

**a**) The DSEC sequence time length (s) and event density (Mevps), where the asynchronous event sequences are sorted in ascending order of the sequence acquisition density and the sequence time length was constrained to contain only the first $\mathcal{T}={10}^{8}\phantom{\rule{0.166667em}{0ex}}\mathsf{\mu}$s (100 s) of the captured event data. (

**b**) The cumulated number of events (Mev) over the first 10 s of the DSEC sequences having the lowest (SeqID: 01), medium (SeqID: 41), and highest (SeqID: 82) acquired event density.

**Figure 7.**The compression ratio (CR) results over the DSEC dataset [34], where the asynchronous event sequences are sorted in ascending order of the sequence acquisition density.

**Figure 8.**The bitrate (BR) results over DSEC [34], where the asynchronous event sequences are sorted in ascending order of the sequence acquisition density.

**Figure 9.**The encoded event density results over the DSEC dataset [34], where the asynchronous event sequences are sorted in ascending order of the sequence acquisition density.

**Figure 10.**The time ratio (TR) results over the DSEC dataset [34], where the asynchronous event sequences are sorted in ascending order of the sequence acquisition density.

**Figure 11.**Encoding runtime results over the DSEC dataset [34], where the asynchronous event sequences are sorted in ascending order of the sequence acquisition density.

**Figure 12.**Decoding runtime results over the DSEC dataset [34], where the asynchronous event sequences are sorted in ascending order of the sequence acquisition density.

**Figure 13.**The relative compression (RC) results for RA results over the DSEC dataset [34], wherein the asynchronous event sequences are sorted in ascending order of the sequence acquisition density.

Method | ZLIB [35] | LZMA [22] | bzip2 [36] | Proposed LLC-ARES | |
---|---|---|---|---|---|

CR | EE order | 2.21 | 3.51 | 2.11 | – |

ST order | 3.22 | 3.92 | 4.14 | 4.3 | |

EBR (bpev) | EE order | 29.65 | 18.91 | 30.50 | – |

ST order | 20.32 | 16.80 | 15.91 | 14.8 | |

${\rho}_{E}$ (Mevps) | ST order | 1.392 | 0.275 | 2.453 | 5.736 |

TR | ST order | 0.133 | 0.027 | 0.246 | 0.531 |

Method | ZLIB [35] | LZMA [22] | bzip2 [36] | Proposed LLC-ARES | |
---|---|---|---|---|---|

Encoding Runtime | EE order | 67.20 $\mathsf{\mu}$s/ev | 210.39 $\mathsf{\mu}$s/ev | 40.91 $\mathsf{\mu}$s/ev | – |

ST order | 44.70 $\mathsf{\mu}$s/ev | 227.27 $\mathsf{\mu}$s/ev | 25.75 $\mathsf{\mu}$s/ev | 10.92 $\mathsf{\mu}$s/ev | |

Decoding Runtime | EE order | 0.78 $\mathsf{\mu}$s/ev | 7.46 $\mathsf{\mu}$s/ev | 16.09 $\mathsf{\mu}$s/ev | – |

ST order | 1.14 $\mathsf{\mu}$s/ev | 5.71 $\mathsf{\mu}$s/ev | 10.58 $\mathsf{\mu}$s/ev | 10.21 $\mathsf{\mu}$s/ev |

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## Share and Cite

**MDPI and ACS Style**

Schiopu, I.; Bilcu, R.C.
Low-Complexity Lossless Coding of Asynchronous Event Sequences for Low-Power Chip Integration. *Sensors* **2022**, *22*, 10014.
https://doi.org/10.3390/s222410014

**AMA Style**

Schiopu I, Bilcu RC.
Low-Complexity Lossless Coding of Asynchronous Event Sequences for Low-Power Chip Integration. *Sensors*. 2022; 22(24):10014.
https://doi.org/10.3390/s222410014

**Chicago/Turabian Style**

Schiopu, Ionut, and Radu Ciprian Bilcu.
2022. "Low-Complexity Lossless Coding of Asynchronous Event Sequences for Low-Power Chip Integration" *Sensors* 22, no. 24: 10014.
https://doi.org/10.3390/s222410014