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### 不等错误保护（Unequal Error Protection, ULP）：图像质量在数据包擦除信道上通过前向错误校正实现优雅降级 #### 摘要与介绍本文提出了不等损失保护 (ULP) 的框架，在该框架中，不同数量的前向错误校正 (Forward Error Correction, FEC) 应用于渐进式数据，以实现图像质量随着数据包丢失率增加时的优雅降级。我们开发了一个简单的算法，可以在 ULP 框架内找到良好的分配方案。本工作中使用了 Set Partitioning in Hierarchical Trees (SPIHT) 编码器，但我们的算法可以应用于任何渐进式压缩方案。此外，我们推广了一种概率质量函数 (PMF) 的预期信道条件的使用，以便系统能够处理几乎任何数据包丢失模型或估计。 #### ULP框架的关键概念 1. **渐进式数据编码**：渐进式编码是指数据被分成多个层次或部分进行传输，允许接收端根据接收到的数据量来逐步恢复原始数据的质量。这种编码技术通常用于图像或视频流，使得即使在较低带宽或高丢包率的情况下也能获得可接受的质量。 2. **前向错误校正 (FEC)**：FEC 是一种在发送端添加冗余信息的方法，以便接收端能够在没有反馈的情况下纠正传输过程中的错误。FEC 能够提高数据传输的鲁棒性，特别适用于无法进行重传请求的实时通信系统。 3. **优雅降级**：在 ULP 框架下，即使部分数据包丢失，图像质量仍然可以保持在一个可接受的水平，从而实现了所谓的“优雅降级”。 #### 算法设计与应用 - **SPIHT编码器**：SPIHT 是一种高效的渐进式图像编码方法，它能够有效地编码图像的细节，并支持不同级别的质量控制。 - **算法实现**：文中提出的一个简单算法可以根据预期的信道条件（例如，数据包丢失率）来确定如何将不同的 FEC 层次应用于 SPIHT 编码后的数据。这一算法的目标是在有限的传输速率下实现最佳的图像质量。 #### 实验结果实验表明，当针对指数分布的数据包丢失模型优化（平均丢失率为20%），并且总传输速率为每像素0.2比特时，即使是40%的数据包丢失，也可以获得较好的图像质量。 #### 关键技术与应用背景 - **联合源/通道编码 (Joint Source/Channel Coding, JSCC)**：这是一种编码策略，旨在同时优化源数据的压缩和传输，以提高整体系统的性能。 - **有损图像传输 (Lossy Image Transmission)**：在这种场景中，数据包丢失是不可避免的，因此需要采取措施确保即使在丢失数据的情况下也能提供一定的服务质量。 - **有损数据包网络 (Lossy Packet Networks)**：这类网络的特点是存在数据包丢失的现象，这对实时通信和多媒体传输构成挑战。 - **数据包擦除信道 (Packet Erasure Channel)**：这是一种理想化的信道模型，其中每个数据包要么完全丢失，要么无错误地到达接收端。 - **数据包丢失 (Packet Loss)**：在网络传输过程中，由于各种原因（如拥塞、错误等）而导致数据包未能到达目的地。 - **优先级编码传输 (Priority Encoding Transmission, PET)**：这是一种编码技术，通过为不同数据分配不同的优先级来优化数据传输。 - **里德-所罗门编码 (Reed-Solomon Coding)**：这是一种广泛使用的 FEC 技术，特别是在存储系统和通信系统中，用于提高数据的可靠性。 #### 结论 ULP 框架为解决有损数据包网络中的图像传输问题提供了一种有效的解决方案。通过合理分配 FEC 层次，可以在有限的带宽资源下实现高质量的图像传输，即使在网络条件不佳的情况下也能保持图像的基本质量。未来的研究可以进一步探索如何针对不同类型的信道条件优化 ULP 算法，以及如何与其他编码技术结合使用以进一步提高传输效率和图像质量。

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IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 18, NO. 6, JUNE 2000 819

Unequal Loss Protection: Graceful Degradation of

Image Quality over Packet Erasure Channels Through

Forward Error Correction

Alexander E. Mohr, Student Member, IEEE, Eve A. Riskin, Senior Member, IEEE, and

Richard E. Ladner, Member, IEEE

Abstract—We present the unequal loss protection (ULP)

framework in which unequal amounts of forward error correction

are applied to progressive data to provide graceful degradation

of image quality as packet losses increase. We develop a simple

algorithm that can find a good assignment within the ULP

framework. We use the Set Partitioning in Hierarchical Trees

coder in this work, but our algorithm can protect any progressive

compression scheme. In addition, we promote the use of a PMF

of expected channel conditions so that our system can work with

almost any model or estimate of packet losses. We find that when

optimizing for an exponential packet loss model with a mean loss

rate of 20% and using a total rate of 0.2 bits per pixel on the

Lenna image, good image quality can be obtained even when 40%

of transmitted packets are lost.

Index Terms—Joint source/channel coding, lossy image trans-

mission, lossy packet networks, packet erasure channel, packet

loss, priority encoding transmission, Reed–Solomon coding,

unequal loss protection.

I. INTRODUCTION

HE INTERNET is a widely deployed network of com-

puters that allows the exchange of data packets. In

traversing the network, a packet is sent from computer to

computer until it arrives at its destination. However, when

the number of packets sent exceeds transmission capacity,

packets are discarded at random, causing loss of data and most

likely decoding failure if the lost data are not retransmitted.

Each packet can be assigned a unique sequence number, so

it is known which packets are received and which are lost. If

the underlying transport protocol does not assign a sequence

number, one or two bytes of the payload can be used to provide

one. When each packet has a unique sequence number, the

receiver can sort the packets according to their transmission

order and any gaps in the sequence are known to be lost packets

Manuscript received May 5, 1999; revised November 5, 1999. This work

was supported by the U.S. Army Research Office under Grant DAAH004-96-1-

0255, an NSF Young Investigator Award, the NSF under Grants EIA-9973531

and CCR-9732828, and by AT&T Bell Laboratories. This paper appearedinpart

in the Proceedings of the Data Compression Conference, Snowbird, UT, March

29–31, 1999.

A. E. Mohr and R. E. Ladner are with the Department of Computer Sci-

ence and Engineering, University of Washington, Seattle, WA 98195-2350 USA

(e-mail: amohr@cs.washington.edu; ladner@cs.washington.edu).

E. A. Riskin is with the Department of Electrical Engineering, University

of Washington, Seattle, WA 98195-2500 USA (e-mail: riskin@ee.wash-

ington.edu).

Publisher Item Identifier S 0733-8716(00)03945-7.

(erasures). The receiver can then take whatever action it deems

best.

In networks in which packets are discarded at random, there

is no way to specify the importance of a particular packet. Usu-

ally, however, the data that we transmit vary in importance. If

we transmit a portrait of a face, for example, data that let us

recognize the person are more important than data that show

the texture of a few strands of hair. If the network is unable to

transmit all of the data, then we would like it to discard the part

describing the hair and retain the part that allows recognition of

the face. Such a network strategy needs to quantify the impor-

tance of different chunks of data and, as channel conditions de-

grade, discard the least important data while retaining the most

important data.

In this paper, we describe the unequal loss protection (ULP)

framework that assigns unequal amounts of forward error cor-

rection (FEC) to images that are compressed with an unmodified

progressive algorithm and are transmitted over lossy packet net-

works without using feedback. After presenting the ULP frame-

work, we give a simple algorithm that can find a good FEC as-

signment within that framework. Our scheme is modular in that

we can use any progressive compression algorithm and have

graceful degradation of image quality with increasing packet

loss rate. We focus on those packet erasure channels without

feedback whose variable loss rates can be expressed as a proba-

bility mass function (PMF). Notable examples are asynchronous

transfer mode (ATM) networks, wireless networks, and UDP-

based transport on the Internet.

II. B

ACKGROUND

In this section, we report previous work on protecting data

from bit errors and packet losses and detail the elements that

will be used in the next section to construct our ULP frame-

work. We begin with an overview of set partitioning in hierar-

chical trees (SPIHT) [1] and explain ways in which it has been

protected for transmission over nonideal channels. We then re-

view the priority encoding transmission [2] scheme for using

Reed–Solomon codes to protect video.

A. Set Partitioning in Hierarchical Trees

An example of a progressive image compression algorithm

is SPIHT [1], an extension of Shapiro’s Embedded Zerotree

820 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 18, NO. 6, JUNE 2000

Wavelet method [3]. These two new algorithms are a signifi-

cant breakthrough in lossy image compression in that they give

substantially higher compression ratios than prior techniques

including JPEG [4], vector quantization [5], and the discrete

wavelet transform [6] combined with quantization. In addition,

the algorithms allow for progressive transmission [7] (meaning

coarse approximations of an image can be reconstructed quickly

from beginning parts of the bit stream), require no training, and

are of low computational complexity.

The SPIHT algorithm uses the 9/7-tap biorthogonal filter in

the discrete wavelet transform [6]. To take advantage of the self-

similarity among wavelet coefficient magnitudes in different

scales, the coefficients are grouped into tree structures called ze-

rotrees. The organization of wavelet coefficients into a zerotree

is based on relating each coefficient at a given scale (parent) to

a set of four coefficients with the same orientation at the next

finer scale (children). Zerotrees allow the prediction of insignif-

icance of the coefficients across scales (that is, if the parent is

insignificant with respect to a given threshold, its children are

also likely to be insignificant) and represent this efficiently by

coding the entire tree at once.

SPIHT groups the wavelet coefficient trees into sets and

orders coefficients by the highest bit plane of the magnitude.

The ordering information is encoded with a set partitioning

algorithm. This algorithm is fully reproduced at the decoder.

The SPIHT algorithm transmits the wavelet coefficients in bit

plane order with most significant bit plane first. For each bit

plane there are two passes. In the first pass, called the dom-

inant pass, coefficients which are significant with respect to

the current threshold are found and coded using the set parti-

tioning method. In the second pass, the subordinate pass, the

precision of all previously significant coefficients is increased

by sending the next bit from the binary representation of their

values. Such refinement allows for progressive-approximation

quantization and produces a fully embedded code, i.e., the

transmission of the encoded bit stream can be stopped at

any point and a lower rate image can still be decompressed

and reconstructed. Additionally, a target bit rate or target

distortion can be met exactly.

B. Joint Source/Channel Coding Using SPIHT

Joint source/channel coding is an area that has attracted

a significant amount of research effort. Despite the fact that

Shannon’s separation theorem [8] states that for a noisy

channel, the source and channel coders can be independently

designed and cascaded with the same results as given by a

joint source/channel coder, complexity considerations have led

numerous researchers to develop joint source/channel coding

techniques. To date, most of this effort has been for fixed rate

codes because they do not suffer from the synchronization

problems that occur with variable rate codes [9]–[11]. (Notable

exceptions that have considered joint source/channel coding

schemes for variable rate codes include work on reversible

variable length codes that can be decoded in both directions

[12]. However, these codes can still have problems with

synchronization.)

SPIHT yields high compression ratios, but images com-

pressed with SPIHT are vulnerable to data loss. Furthermore,

because SPIHT produces an embedded or progressive bit

stream, meaning that the later bits in the bit stream refine earlier

bits, the earlier bits are needed for the later bits to even be

useful. However, SPIHT’s impressive performance is leading

researchers to consider transmitting images compressed with

SPIHT over lossy channels and networks.

C. Prior Work on Transmitting SPIHT over Noisy Channels

Sherwood and Zeger [13] protected images compressed with

SPIHT against noise from the memoryless binary symmetric

channel with rate-compatible punctured convolutional (RCPC)

codes [14] with good results. They extended this work to images

transmitted over the Gilbert–Elliott channel (a fading channel)

in [15]. In the latter case, they implement a product code of

RCPC and Reed–Solomon codes and find that this outperforms

the work in [13] even for the binary symmetric channel.

Rogers and Cosman were the first to consider the transmis-

sion of images compressed with SPIHT over packet erasure

networks [16]. They used a fixed-length packetization scheme

called packetized zerotree wavelet (PZW) compression to

transmit images compressed with a modified SPIHT over lossy

packet networks. The algorithm does not use any channel

coding. They implemented a scheme to fit as many complete

wavelet trees (i.e., one coefficient from the lowest frequency

wavelet subband along with all its descendants) as possible

into a packet. The algorithm degrades gracefully in the pres-

ence of packet loss because the packets are independent. If a

packet is lost, they attempt to reconstruct the lowest frequency

coefficients from the missing trees of wavelet coefficients by

interpolating from neighboring low frequency coefficients that

have been correctly received by the decoder. To simplify their

algorithm, they used fewer levels of wavelet decomposition

and removed the arithmetic coder from the SPIHT algorithm.

The modification of the SPIHT algorithm caused a decrease of

about 1.1 dB in the PSNR for the Lenna image coded at 0.209

bits per pixel for the case of a channel without losses.

These two schemes were combined into a hybrid scheme in

[17]. The authors consider the case where, in addition to packet

loss, packets can arrive with bit errors in them. They use channel

coding to correct bit errors and PZW to conceal packet losses. If

they cannot correct all of the bit errors in a packet, they consider

the packet to be erased. The hybrid scheme shows resilience to

packet loss, bit errors, and error bursts. It is still based on the

modifiedSPIHT algorithm used in [16], which does not perform

as well as the original SPIHT algorithm.

In recent work, Chande and Farvardin presented an unequal

error protection algorithm for progressive transmission over bit

error channels [18]. They assume that the bit stream can only be

decoded up to the first uncorrectable error. They suggest max-

imizing the average useful source coding rate as an optimiza-

tion criterion, because a longer prefix of the bit stream yields

higher reconstructed image quality when decoded [18]. They

use RCPC codes for bit errors. They use a dynamic program-

ming approach to find the optimal code policy for each bit rate.

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