^{1}

^{1}

^{2}

^{3}

^{4}

^{5}

^{1}

^{2}

^{3}

^{4}

^{5}

First unequal error protection (UEP) proposals date back to the 1960's (Masnick and Wolf; 1967), but now with the introduction of scalable video, UEP develops to a key concept for the transport of multimedia data. The paper presents an overview of some new approaches realizing UEP properties in physical transport, especially multicarrier modulation, or with LDPC and Turbo codes. For multicarrier modulation, UEP bit-loading together with hierarchical modulation is described allowing for an arbitrary number of classes, arbitrary SNR margins between the classes, and arbitrary number of bits per class. In Turbo coding, pruning, as a counterpart of puncturing is presented for flexible bit-rate adaptations, including tables with optimized pruning patterns. Bit- and/or check-irregular LDPC codes may be designed to provide UEP to its code bits. However, irregular degree distributions alone do not ensure UEP, and other necessary properties of the parity-check matrix for providing UEP are also pointed out. Pruning is also the means for constructing variable-rate LDPC codes for UEP, especially controlling the check-node profile.

Source-coded data, especially from scalable video and audio codecs, come in different importance levels. Thus, data has to be protected differently. We discuss different means of achieving unequal error protection (UEP) properties on the physical level and by different coding schemes. In physical transport, we concentrate on multicarrier modulation (OFDM, DMT) presenting bit-allocation options realizing UEP properties, additionally using hierarchical modulation, as well. Modulation-oriented UEP solutions prove to be a suitable and very flexible tool to define arbitrary protection levels, if access to the actual physical transport is possible. Other options are provided by channel coding and in here, we will especially discuss Turbo and LDPC codes providing UEP. The common approach for implementing UEP properties as in standard convolutional codes would certainly be puncturing [

Pruning in an LDPC context would mean eliminating variable nodes in the bipartite Tanner graph setting these variables to known values, for example, zero. This will in turn modify the check degree of connected check nodes. It will serve as a tool for designing check-node degree distributions for a given UEP profile.

After some more introductory remarks on UEP for video coding in Section

A treatment of pruned Turbo codes will follow in Section

We also study LDPC codes with an irregular variable-node profile in Section

Finally, we consider modifications of the check-node profile of LDPC codes by pruning in Section

Note that whenever error-ratio performances are shown, they will be over

Before we actually discuss different UEP solutions, we should deliberate shortly how we should relate source coding qualities given by spatial and temporal resolution and signal-to-noise ratio margin separations or error rates. We start referencing a work by Huang and Liang [

Huang and Liang [

For a rate-distortion relation, Huang and Liang write the total rate as

This is a treatment that is reasonable for rate-compatible punctured convolutional codes [

In the following, we will describe options that we investigated to realize UEP in multicarrier hierarchical modulation, Turbo-, and LDPC-coding. These schemes will prove to be very flexible, allowing the realization of arbitrary SNR level increments between quality classes.

We begin our treatment with modulation-based UEP realizations, starting from hierarchical modulation without bit-loading, followed by bit-loading, to finally combine both concepts in bit-loaded hierarchical multicarrier modulation. We use different bit-loading algorithms to give a flavor of options that are possible, although space limitations will not allow to study all UEP modifications of known bit-loading algorithms.

In hierarchical modulation, also known as embedded modulation [

Hierarchical quadrature amplitude modulation (QAM): (a) 4/16/64-QAM and (b) 2/4/8-QAM.

A 4-QAM (

A BPSK (

Figure

SER performance for 2/4/8 hierarchical QAM (defined in Figure

Traditionally, bit-loading algorithms have been designed to assure the highest possible link quality achieving equal error probability. This results in performance degradations in case of variable channel conditions (no graceful degradation). In contrast, UEP adaptation schemes [

As in the original algorithm, the quantization error

How should now different protection classes be mapped onto the given subcarriers? An iterative sorting and partitioning approach has be proposed in [

The

In [

If the target bit-rate

Else, if the maximum number of iterations is achieved without fulfilling

The main drawback of the previous two methods [

Figure

SER performance for the modified Chow algorithm assuming 3 different classes with margin separations of 3 dB, and 6144 bits on 2048 subcarriers with two scenarios:

For the optimal power bit-loading algorithms (like Hughes-Hartogs), we opt for hierarchical modulation to realize UEP classes [

In here, we are going to describe the complete power minimization hierarchical bit-loading algorithm. This algorithm can be considered as a margin-adaptive bit-loading defined as

Initially, allocate

Set

Compute the incremental power steps

Find the minimum

Increment the power of this subcarrier

If the target bit-rate of the

the sum of the powers

else, stop and go to (

If the target bit-rate of the

if the sum of the energy is less than the target energy

else, stop the iterations for this class.

Scale-up the allocated energy

The matrix

Figure

SER performance in Rayleigh fading for the modified Hughes-Hartogs algorithm with adaptive hierarchical QAM assuming 3 different classes with a margin separation of 3 dB. In total, this figure has 6144 bits on 2048 subcarriers with two scenarios:

An example of combining hierarchical modulation schemes with Turbo coding of different rates is given in [

In this paper, we only focus on (almost) capacity-achieving codes. Turbo codes are known for their error-floor behavior, nevertheless they are suited for smaller codeword lengths, that is, interleaver sizes. If the error floor is an issue, outer Reed-Solomon codes may be applied. There are, of course, manyfold options with smaller codeword lengths or delays, such as rate-compatible convolutional codes based on puncturing, which we are to some extent addressed inside the following Turbo-code section. Just to mention another example, one may also think of multilevel coded modulation with corresponding rate choices according to the desired SNR steps [

In this section, we describe methods of achieving unequal error protection with convolutional codes which can later be applied in Turbo codes. A straightforward approach of varying the performance of a convolutional code is puncturing, that is, excluding a certain amount of code bits from transmission and, thus, increasing the code rate

A possible pruned input sequence to a 2-input encoder with certain positions fixed to 0 could be

Set of bit-error rate curves of pruned and punctured Turbo codes built from RSC codes (for parameters, see the appendix).

When performing a computer search for a suitable pruning scheme, it is usually not sufficient to study pruning patterns alone. Additionally, it has to be ensured that at interval boundaries between blocks of different protection levels, the states at joint trellis segments are the same as already required in rate-compatible punctured convolutional codes [

Concerning the minimum distance of the subcode, it is in either case greater than or equal to the minimum distance of the mother code since, as stated above, both codes can be illustrated by the same trellis. Fixing certain probabilities of a zero to be infinity means pruning those paths corresponding to a one. Either, if the minimum weight path is pruned, the minimum distance of the code is increased or if it is not pruned, the minimum distance stays the same.

The proposed technique is in a way dual to puncturing with comparable complexity. Puncturing increases the rate by erasing output bits, whereas pruning reduces it by omitting input bits (fixing its value). With puncturing, there is no knowledge about the erased bits in the decoding. With pruning, we add perfect knowledge about certain bits and may enhance the decoding performance in iterative decoding through increased extrinsic information. Occasional pruning has also once been used to improve the NASA serial concatenation of convolutional and Reed-Solomon codes in [

We ran an exhaustive computer search in order to find mother codes together with different pruning patterns which behave well in iterative decoding. We used EXIT charts [

The code table shows that the higher the degree of pruning (and the lower the code rate), the larger is the minimum distance. This is natural, since with a large number of constraints, it is more likely that the minimum distance path is erased.

Irregular low-density parity-check (LDPC) codes are very suitable for UEP, as well, and can be designed appropriately according to the requirements. Irregular LDPC codes provide UEP simply by modification of the parity-check matrix and a single encoder and decoder may still be used for all bits in the codeword. The sparse parity-check matrix

Based on an optimized degree distribution pair of

Since the degree distribution pairs are equal for all algorithms, a more detailed definition of the degree distribution is necessary. The multi-edge type generalization [

Figure

Detailed check-node degree distribution coefficients for the codes constructed by the ACE and the PEG-ACE algorithms.

Figure

Check node

Distance of variable node

To confirm that the detailed check-node degree distribution is the key to the UEP capability of a code, a modification of the nonUEP PEG-ACE algorithm, which makes it UEP-capable, is presented. By constraining the edge selection procedure to allow only certain check-nodes to be connected, the resulting detailed check-node degree distribution is made similar to that of the ACE code. The bit-error rates of the codes constructed by the modified PEG-ACE, the original PEG-ACE and the ACE algorithm are shown in Figure

BER of the

Further work is currently done along protograph constructions and and multi-edge type LDPC codes [

In Figure

We consider a check-node to belong to a certain bit-node (priority) class

Using the detailed representation of the LDPC code [

Figure

Pruning in the Tanner graph to exhibit UEP properties

In the following, we describe the iterative pruning procedure in some more detail.

Let the relative portion of bits devoted to a class

Any pruned bit must not be linked with a check-node of degree already identical to the lower limit of a priori chosen degree distributions.

Unvoluntary pruning shall be avoided, meaning that a column of the parity-check matrix

The chosen code rate

Convergence at a desired signal-to-noise ratio (near the Shannoncapacity limit) must be ensured, typically by investigating EXIT charts [

A stability constraint [

In an iterative procedure,

Figure

BERs of concentrated and nonconcentrated pruned check-irregular codes of rate 1/3 and length 1000 after 30 iterations for

Optimizations to obtain unconcentrated (degrees for checks between 2 and 6) and almost concentrated (degrees for checks between 4 and 6) degrees codes were performed to compare the performances.

The decoder is using the pruned parity-check matrix of the mother code. The check-node profiles are given in Table

Check-node profiles of concentrated and nonconcentrated codes used in Figure

Check profile of the almost concentrated code

2 | 3 | 4 | 5 | 6 | |
---|---|---|---|---|---|

Class 1 | 0 | 0 | |||

Class 2 | 0 | 0 | |||

Class 3 | 0 | 0 |

Check profile of the unconcentrated code

2 | 3 | 4 | 5 | 6 | |
---|---|---|---|---|---|

Class 1 | |||||

Class 2 | |||||

Class 3 |

List of good codes with constraint length

conv. mother code | pruning pattern | area | |||||
---|---|---|---|---|---|---|---|

4 | |||||||

4 | |||||||

4 | |||||||

4 | |||||||

6 | |||||||

6 | |||||||

5 | |||||||

5 | |||||||

5 | |||||||

5 | |||||||

6 | |||||||

6 | |||||||

7 | |||||||

8 | |||||||

This paper has pointed out manifold options for realizing unequal error protection, especially new concepts developed recently. UEP in multicarrier physical transport is very easy to realize and the design is very flexible allowing for arbitrary SNR margins. In UEP Turbo or LDPC coding, the coding scheme has to be optimized in advance, that is, a code search is necessary and the performances have to be investigated beforehand (EXIT charts, simulations). Pruning and puncturing also offer quite some flexibility in choosing the code rate, but the actual performances are only obtained after the code-design and evaluation steps. However, in digital transport without access to the physical channel, the only option is UEP coding.

When the channel changes its frequency characteristic, the margins between the priority classes will be modified in UEP bit allocation, even if a more robust SNR sorting is used. In UEP Turbo or LDPC coding, the margins will more or less be preserved due to the large interleaver.

Generator matrix of the mother code:

Puncturing and pruning pattern:

Some of this work was part of the FP6/IST Project