Multiple description transform coded transmission over OFDM broadcast channels

Abstract

We consider image transmission using multiple description transform coding (MDTC) over orthogonal frequency division multiplexed (OFDM) wireless broadcast channels, where the system may not have any feedback on channel gains. We investigate the redundancy allocation in MDTC–OFDM system, physical layer frequency diversity, and decoding strategies to maximize the quality of reconstruction. Via mathematical analysis, supported by MATLAB simulations, we show that, error resilience of the descriptions can be increased by suitable assignment of coding redundancy in the transform modules at the source, which can be further optimized if the channel characteristics are known at the transmitter. Additionally, the relative performance of the MDTC–OFDM system is studied with respect to a competitive approach, called forward error correction based multiple description coding (MDC) over OFDM, where we show that, for the same redundancy assignment, the MDTC based system performs better under harsh channel conditions.

Introduction

There are three types of coding normally practiced for image/video content: non-progressive coding, progressive (layered) coding, and multiple description coding (MDC). In MDC, the MD coder generates multiple descriptions or message blocks from the source content. The generated descriptions are such that they are correlated with each other. This correlatedness feature is introduced by adding some controlled redundancy or extra bits to the compressed source data. This process helps to estimate the lost (corrupted) descriptions from the correctly received ones and thus retransmissions can be avoided  [1], but it is at the cost of a reduced compression efficiency. MDC is a more robust technique for wireless environments, as an MDC receiver can decode the data with a low but acceptable image quality even if some of the descriptions are lost  [2].

At the physical transmission level, orthogonal frequency division multiplexing (OFDM) is used in many current wireless communication systems, as it provides an opportunity to exploit the diversity in frequency domain by providing a number of sub-carriers, which can work as multiple flat fading channels for applications dealing with multiple bit streams.

Combinedly, MDC at the source along with OFDM at the physical layer is an interesting alternative image/video coding technique to combat bursty packet losses over wireless channels, and it is especially promising for applications where retransmission is unacceptable.

The simplest way to produce multiple descriptions is to partition the raw source content into the required number of sets and compress them independently. For description recovery, interpolation techniques are used  [3]. Scalar quantization based MDC (called MDSQ) is another technique that was introduced in  [4]. The recent advancements in this area are Gram–Schmidt orthogonalization based multiple description quantization (MDQ)  [5] and the one via delta-sigma modulation  [6]. Another recent development is lattice vector quantization based multiple descriptions (MDLVQ) generation  [7], [8], that exploits the correlation among the source samples. Multiple description transform coding (MDTC) is another variant of MDC, that was introduced in  [9], [10] and further extended in  [11]. In MDTC, a correlating transform is used to introduce dependency among the coefficients (by adding redundancy or extra bits per coefficient), so that they can be estimated from each other, albeit with some distortion in the reconstructed data at the receiver. Besides the above techniques at the source level, forward error correction (FEC) based joint source-channel coding, called FEC-MDC  [12], [13], has been another popular approach that works based on the channel state information (CSI). Among these several variants, namely, quantization based (e.g., MDSQ, MDVQ), transformed based (i.e., MDTC), and FEC based MDC, MDTC has the benefit of higher coding efficiency relative to MDQ techniques   [10]. MDTC also enjoys simplicity and widespread compatibility with any source compression algorithm compared to FEC–MDC   [12], [9], [13].

The use of FEC variants for transmission of delay constrained contents, such as image/video, with or without involving MDC has been studied in different systems. For example, for video transmission over wireless  [14], packet interleaving is combined with dynamic FEC to combat burst errors. Particularly, the packet interleaving and FEC were adapted with respect to packet deadlines, packet priority, and buffer occupancy, to improve the quality of the delivered content. In  [15], unequal error protection (UEP) for progressively encoded image transmission over single carrier wireless system with Rayleigh fading channels was studied where hierarchical modulation techniques were considered. The study in  [16] provided a lucid description of performance and complexity issues associated with MDC and UEP–FEC schemes for image and video transmissions.

For image frame transmission, MDTC is generally applied on a compressed frame. It could be based on either discrete cosine transform (DCT) or discrete wavelet transform (DWT). In  [11], a general framework based on square linear transform on MDTC to generate more than two descriptions from DCT coefficients was presented. For a two-description case (i.e., 2×2 transform), a simple optimal transform was proposed that produces a balanced rate for the two channels, where the redundancy-distortion trade-off can be controlled by a single parameter in the transform matrix. For realizing MDC with more than two descriptions, the authors also proposed a cascade structure for MDTC to maintain the ease of design. To our best knowledge, the important aspect of optimal redundancy allocation, which helps maximize the description recovery in the face of transmission errors with the minimum possible overhead of data rate, is still missing in the literature.

Between DCT based and DWT based MDTC variants, the latter was shown to be more robust to noise  [17]. DCT-MDTC principles were applied on DWT images in  [17]. The new system was called DWT-MDTC. The relative performance of DCT-MDTC and DWT-MDTC under varying number of received descriptions showed that the DWT–MDTC performs better under lossy scenarios. Along this line, our interest is to analytically formulate the MDTC estimation and distortion associated with the losses by accounting the actual physical channel behavior.

As prior research has demonstrated, physical layer diversity also has an important role along with MDC for an optimum system performance  [18], [19]. Several physical layer works, e.g., priority based protection scheme  [20], rate-distortion performance  [21], optimal rate allocation in MD coded transmission  [22], studied the channel diversity issues based on the premise of independent erasure channels. FEC-based MDC over OFDM (FEC-MDC–OFDM) system performance was evaluated  [23] and mathematically analyzed  [24] under the block fading channels. The study was extended in frequency selective fast fading channel environment  [25]. The application of FEC–MDC for scalable video transmission over OFDM channels was also carried out in  [26]. The discussion on video transmission is however out of scope of this paper. In these studies cross-layer diversity gain was obtained from frequency selectivity of fading channels. For distortion performance measure in  [23], [24], [25], the number of descriptions was set equal to the number of OFDM sub-channels. However, the description loss probability in such fading environments is highly dependent on the application layer diversity. In other words, characterizing the distortion function in FEC-based MDC over OFDM channels would be more involved in a frequency selective fading environment if the number of descriptions is much less than the number of sub-channels. Also, the error protection overhead added to each application layer coded (layered) description in FEC-based MDC is dependent on image/video characteristics (e.g., contrast, frame rate).

Although MDTC–OFDM system offers a simpler alternative to MD quantization variants and FEC-based MDC, the performance of MDTC with two or more descriptions over OFDM channels has not been adequately studied in the literature. These considerations along with the lack of CSI feedback in broadcast channels motivate us to investigate the MDTC performance over fading channels with OFDM-based physical layer.

In this paper, the optimization of DWT–MDTC transmission over OFDM fading broadcast channels is investigated with an implicit assumption of a symmetric MDC (where the descriptions are equally important). The major contributions in this paper are the following:

• to aid applicability of the proposed MDTC–OFDM scheme on any image frames, a generalized parametric function, which models how the image is compressed based on the image frame’s quality factor (e.g., sharpness, contrast), is introduced;

• a channel-aware MDTC–OFDM system is designed by optimally assigning the redundancy to minimize the average distortion. It is shown that the error resilience of the descriptions can be increased by the suitable assignment of coding redundancy in the transform modules at the source and by exploiting physical layer frequency diversity and channel feedback. It may be noted that, optimum redundancy allocation in MDC descriptions for a given total redundancy is critical for minimized distortion of the application content at the receiver;

• a sub-optimal method, which is solely based on the quality factor of the image and the redundancy allocation at the source, is developed for channel-oblivious MDTC–OFDM system for broadcast channels. The performance of the proposed method for the channel-oblivious MDTC–OFDM system is compared with that of the channel-aware MDTC–OFDM system. In addition, an efficient MDTC decoding (estimation) technique is proposed to maximize the image reception quality.

A comparative study of the proposed MDTC–OFDM system with a competitive scheme (FEC-MDC–OFDM) shows that the MDTC–OFDM system performs better under harsh channel condition.

The rest of the paper is organized as follows. Section  2 describes the MDTC–OFDM system model, the proposed parametric model that generically represents a compressed source, the cascade structure for the MDTC along with the estimation approach, the channel model, and MDTC descriptions mapping over the OFDM channels. Section  3 contains the distortion analysis, fading channel dependent error performance, and optimization formulation on redundancy allocation. Section  4 presents the numerical optimization procedure and the results on channel feedback based optimum redundancy allocation and channel-oblivious sub-optimal redundancy allocation performance, followed by a comparative performance study of MDTC–OFDM and FEC-MDC–OFDM systems in Section  5. The paper is concluded in Section  6.