A 2-level FEC mechanism joint with cross-layer superposition coded multicast for robust IPTV service over WiMAX

Abstract

This paper proposes a framework with scalable video coding (SVD) at the source joint with a 2-level Forward Error Correction (FEC) at the channel and superposition modulation for efficient IPTV video multicasting over IEEE 802.16 (or WiMAX), called 2-level FEC joint with Multiple Description Coding (2FMDC). Multiple description coding (MDC) on SVD that generates multi-resolution of a video joint with superposition modulation (multi-resolution modulation) can overcome the channel diversity problem in wireless multicasting. In this framework, we use a 2-level FEC that enables a Subscriber Station (SS) to recover the lost frame and receive the video with more quality. The 2-level FEC denotes vertical FEC joint with horizontal FEC. Our proposed method applies identical redundancy compared with similar methods to the network traffic. Performance evaluation results demonstrate that using our proposed framework, an SS can achieve better video quality under multi-user channel diversity.

Appendix: Computing the probability of receiving high-quality layer video [5]

To compute the probability of receiving quality layers, the following steps should be performed:

Step 1: The SNR at SS m, γ _l,m , is computed by [5]:

$$ \gamma_{l,m} = {\frac{{cd_{m}^{ - \alpha } p_{l} \left| {h_{m}^{2} } \right|}}{{N_{0} W + \sum\limits_{i = l + 1}^{L} {cd_{m}^{ - \alpha } p_{i} \left| {h_{m}^{2} } \right|} }}}, $$

(15)

where p _l is power allocated by the BS to the modulated signal of quality layer l, L is the number of quality layers, d _m is the distance between SS-m and the BS, α is the path loss exponent (α = 4 for an urban area and 3 for a rural area), c is a constant, $\left| {h_{m}^{2} } \right|$ is a random number with a Rayleigh fading distribution, W is the effective bandwidth seen by the SS, and N₀ is the average background noise power [5].

The transmission rate (bits/second) of a modulation scheme must have the following condition:

$$ R_{M,l} \ge {\frac{{\left( {b_{l} - b_{l - 1} } \right)}}{{k_{l} \times t}}}, $$

(16)

where R _M,l is the transmission rate (bits/second) of a modulation scheme within the set {BPSK, QPSK, 16QAM, 64QAM}; b _l is the up boundary of the quality layer l in bits; k _l is the value for RS code on layer l, and t is the duration of one timeslot assigned to a multicast transmission by a scheduling policy. Then, the required condition to use a specific modulation scheme M at layer l, R _M,l,m is:

$$ R_{M,l,m} (\gamma_{l,m} ) = \left\{ {\begin{array}{*{20}c} {64 \, QAM,} \hfill & {{\text{if }}18.5 \, dB \le \gamma_{l,m} } \hfill & {\text{and}} \hfill & {R_{M,l} = 64 \, QAM} \hfill \\ {16 \, QAM,} \hfill & {{\text{if }}11.5 \, dB \le \gamma_{l,m} } \hfill & {\text{and}} \hfill & {R_{M,l} = 16 \, QAM} \hfill \\ {QPSK,} \hfill & {{\text{if }}6 \, dB \le \gamma_{l,m} } \hfill & {\text{and}} \hfill & {R_{M,l} = QPSK} \hfill \\ {BPSK,} \hfill & {{\text{if }}3 \, dB \le \gamma_{l,m} } \hfill & {\text{and}} \hfill & {R_{M,l} = BPSK} \hfill \\ {{\text{fail}},} \hfill & {\text{otherwise}} \hfill & {} \hfill & {} \hfill \\ \end{array} } \right., $$

(17)

If R _M,l,m fails, different parameters should be modified in order to satisfy R _M,l,m .

Step 2: The expected BER e _l,m for receiving layer l at SS m depends on the SNR of that layer and is approximately given by:

$$ e_{l,m} (R_{M,l,m} ,\gamma_{l,m} ) = \left\{ {\begin{array}{*{20}c} {Q\left( {\sqrt {2\gamma_{l,m} } } \right),} \hfill & {\text{if}} \hfill & {R_{M.l,m} = BPSK} \hfill \\ {Q\left( {\sqrt {\gamma_{l,m} } } \right),} \hfill & {\text{if}} \hfill & {R_{M.l,m} = QPSK} \hfill \\ {\frac{1}{4}\left[ {Q\left( {\sqrt {{\frac{{\gamma_{l,m} }}{5}}} } \right) + 3Q\left( {\sqrt {{\frac{{\gamma_{l,m} }}{5}}} } \right)} \right] + \frac{1}{2}Q\left( {\sqrt {{\frac{{\gamma_{l,m} }}{5}}} } \right),} \hfill & {\text{if}} \hfill & {R_{M,l,m} = 16QAM} \hfill \\ {\frac{1}{12}\left[ {Q\left( {\sqrt {{\frac{{\gamma_{l,m} }}{21}}} } \right) + Q\left( {3\sqrt {{\frac{{\gamma_{l,m} }}{21}}} } \right) + Q\left( {5\sqrt {{\frac{{\gamma_{l,m} }}{21}}} } \right) + Q\left( {7\sqrt {{\frac{{\gamma_{l,m} }}{21}}} } \right)} \right]} \hfill & {} \hfill & {} \hfill \\ { + \frac{1}{6}Q\left( {\sqrt {{\frac{{\gamma_{l,m} }}{21}}} } \right) + \frac{1}{6}Q\left( {3\sqrt {{\frac{{\gamma_{l,m} }}{21}}} } \right) + \frac{1}{12}Q\left( {5\sqrt {{\frac{{\gamma_{l,m} }}{{21}}}} } \right)} \hfill & {} \hfill & {} \hfill \\ { + \frac{1}{12}Q\left( {7\sqrt {{\frac{{\gamma_{l,m} }}{21}}} } \right) + \frac{1}{3}Q\left( {\sqrt {{\frac{{\gamma_{l,m} }}{21}}} } \right) + \frac{1}{4}Q\left( {3\sqrt {{\frac{{\gamma_{l,m} }}{21}}} } \right)} \hfill & {} \hfill & {} \hfill \\ { - \frac{1}{4}Q\left( {5\sqrt {{\frac{{\gamma_{l,m} }}{21}}} } \right) - \frac{1}{6}Q\left( {7\sqrt {{\frac{{\gamma_{l,m} }}{21}}} } \right) + \frac{1}{6}Q\left( {9\sqrt {{\frac{{\gamma_{l,m} }}{21}}} } \right)} \hfill & {} \hfill & {} \hfill \\ { + \frac{1}{12}Q\left( {11\sqrt {{\frac{{\gamma_{l,m} }}{21}}} } \right) - \frac{1}{12}Q\left( {13\sqrt {{\frac{{\gamma_{l,m} }}{21}}} } \right),} \hfill & {\text{if}} \hfill & {R_{M,l,m} = 64QAM}, \hfill \\ \end{array} } \right. $$

(18)

where Q() is a Q function defined by:

$$ Q(\alpha ) = \frac{1}{2} - \frac{1}{2}erf\left( {{\frac{\alpha }{\sqrt 2 }}} \right), $$

(19)

Step 3: Probability that the whole column of PUs of layer l in a partial MDC packet are getting lost or erroneous at SS-m can be derived as [5]:

$$ \varepsilon_{l,m} = 1 - (1 - e_{l,m} )^{({b_{l} - b_{l - 1} })/k_{l}}, $$

(20)

Step 4: The probability of obtaining N − K _l or fewer erasures in N partial MDC packets of layer l at SS m for a GoF can be approximated by [5]:

$$ P_{l,m} = \Pr \left\{ {F_{l} \le N - K_{l} } \right\} = \sum\limits_{j = 0}^{{N - K_{l} }} {\left( \begin{gathered} N \hfill \\ j \hfill \\ \end{gathered} \right)} (\varepsilon_{l,m} )^{j} (1 - \varepsilon_{l,m} )^{N - j} , $$

(21)

where F _l denotes a random variable that represents the number of packet erasures in a group of N partial MDC packets at layer l.

In addition, note that the average number of receivable/recoverable bitstreams of layer l, denoted by T _l,m , in a GoF obtained by SS-m can be calculated by:

$$ T_{l,m} = (b_{l} - b_{l - 1} )\prod\limits_{i = 1}^{l} {P_{i,m} } , $$

(22)

Then, the total average number of receivable/recoverable video bitstreams T _m (in bits) of a GoF with L layers by SS-m can be expressed by:

$$ T_{m} = \sum\limits_{l = 1}^{L} {T_{l,m} } , $$

(23)

Example 4:

For example under channel SNR of 20 dB (obtained by Eq. 15), b ₁ = 198,771, b ₂ = 201,565, N = 255, K ₁ = 243, K ₂ = 230, S = 8, and S _c  = 16, the probability of receiving high quality layer at modified layer MDC is computed as follows:

• Compute BER at layer 2 with modulation scheme 16QAM by Eq. 18, i.e., e _2,m = 0.0171. Calculate $\varepsilon_{l,m}$ = 0.8122, the probability that the whole column of PUs in a partial MDC packet are lost or erroneous using Eq. 20.

• Compute the probability of receiving high quality layer, P _2,m = 1.3666 × 10⁻¹³⁵ by Eq. 21.

• Compute the total number of receivable video bitstream, T _m  = 198,871 by Eq. 23.