Improved Joint Source/ Channel Decoding of VLCs · Amin ZRIBI Improved Joint Source/ Channel decoding of VLCs. Overview of Joint Source/ Channel ... Decoding algorithm 1. Calculate

Improved Joint Source/ Improved Joint Source/ Channel Decoding of VLCs

Amin [email protected]

Ramesh PyndiahRamesh [email protected]

Sonia [email protected]

Frédéric [email protected]

May 28, 2009

Contents

� Overview of Joint Source/ Channel decoding of VLCs• State of the art• Problem Statement• Problem Statement• Sequence estimation for VLC decoding

� Length-constrained Chase-like decoding of VLCs• Decoding algorithm• Simulation results• Comparison to trellis-based decoding

� Iterative Chase -like decoding of VLCs with FEC

page 1

Iterative Chase -like decoding of VLCs with FEC• Bit reliabilities definition• The case of RSC code• The case of LDPC code

� Conclusions and future work

Amin ZRIBI Improved Joint Source/ Channel decoding of VLCs

Overview of Joint Source/ Channel decoding of VLCs

� State of the art

Amin ZRIBI Improved Joint Source/ Channel decoding of VLCspage 2

� State of the art� Problem Statement� Sequence estimation for VLC decoding

State of the art

� VLC-encoded streams are very sensible to transmissi on errors (synchronization loss and error propagation)

� Joint Source/ Channel decoding schemes:

page 3 Amin ZRIBI Improved Joint Source/ Channel decoding of VLCs

State of the art


� Joint Source/ Channel decoding schemes:• Robust entropy coding techniques (Sync. Markers, EREC, RVLC…)


State of the art


� Joint Source/ Channel decoding schemes:• Robust entropy coding techniques (Sync. Markers, EREC, RVLC…)• Use of Forward Error Correction


State of the art


� Joint Source/ Channel decoding schemes:• Robust entropy coding techniques (Sync. Markers, EREC, RVLC…)• Use of Forward Error Correction • Trellis or state-machine VLC representation (channel decoding

techniques)

- Performance upgrade

page 3

- Performance upgrade

- Prohibitive complexity for real applications

- Not easy to adapt with various VLC versions (adaptive, contextual)

Amin ZRIBI Improved Joint Source/ Channel decoding of VLCs

Problem Statement

� Conception of a decoder which:• has a reasonable complexity,• has good error correcting performance,• and is adaptable to all VLC versions.


Problem Statement

� Conception of a decoder which:• has a reasonable complexity,• has good error correcting performance,• and is adaptable to all VLC versions.

Instantaneous hard

input VLC decoding

ML soft input sequence

estimation


� Hypothesis:• To improve decoding: The space search should obey to length conditions:

source symbol sequences of length L corresponding to compressed bit streams of lengths l.

• Suboptimal sequence estimation: Chase-like decoding.

Sequence estimation for VLC decoding

VLC AWGN s(L) b(l) r(l) VLC prefix

Classical decoding

)ˆ(ly )ˆ(ˆ LsVLC encoder

AWGN Channel

s(L) b(l) r(l) VLC prefix decoding

)ˆ(ly )ˆ(ˆ Ls


Sequence estimation for VLC decoding

r(l)

Proposed decoding with length constraints

)(ˆ lb )(ˆ LsVLC AWGN s(L) b(l) r(l) ML estimation

Length validity ?a priori information

VLC prefix decoding

)(ˆ lb )(ˆ Ls

BPSK modulation, we maximize:

∑2)-(l jhr

VLC encoder

AWGN Channel

s(L) b(l)


•• , nj : Gaussian noise sample with zero mean and variance

∑1

2

2

))(log()2

)-((

l

j

jkj

k Phr

M=

+= ksσ

)(BPSK= jk

jk bh

jj

kj nhr += 2σ

Length-constrained Chase-like decoding of VLCs

� Decoding algorithm


� Decoding algorithm� Simulation results� Comparison to trellis-based decoding

Decoding algorithm

1. Calculate the hard decision vector ,

determine the positions of the q least reliable samples ,

y

2. determine the positions of the q least reliable samples ,

3. form test patterns for ,

4. from test sequences with ,

5. Apply standard VLC decoding to test sequences. If a

sequence is length -valid we store and we calculate its

Qi <≤0,it qQ 2=

Qi <≤0,iz ijj

ij tyz ⊕=


sequence is length -valid we store and we calculate its

metric,

6. The decoded stream is the ML stored sequence .

Simulation results

� Results for different codes• L = 128 symbols

i pi C1 C2 C3

0 0.5 0 0 0

1 0.25 1 0 1 0 1 1

2 0.125 1 1 1 1 1 0 1 0 1

VLC table

• q = 4 bits


2 0.125 1 1 1 1 1 0 1 0 1

3 0.125 1 1 0 1 1 1 0 1 0 0 1

lav 1.75 1.875 1.875

RVLC 1.0 0.933 0.933

Simulation results


i pi C1 C2 C3

0 0.5 0 0 0

1 0.25 1 0 1 0 1 1

2 0.125 1 1 1 1 1 0 1 0 1

VLC table

• q = 4 bits


2 0.125 1 1 1 1 1 0 1 0 1

3 0.125 1 1 0 1 1 1 0 1 0 0 1

lav 1.75 1.875 1.875

RVLC 1.0 0.933 0.933

Simulation results


i pi C1 C2 C3

0 0.5 0 0 0

1 0.25 1 0 1 0 1 1

2 0.125 1 1 1 1 1 0 1 0 1

VLC table

• q = 4 bits


2 0.125 1 1 1 1 1 0 1 0 1

3 0.125 1 1 0 1 1 1 0 1 0 0 1

lav 1.75 1.875 1.875

RVLC 1.0 0.933 0.933

Simulation results

� Results for different test pattern lengths• Code C3

• L = 128 symbols• q = 1, 2, 3, 4 and 8 bits


Simulation results

� Results for different test pattern lengths• Code C3

• L = 128 symbols• q = 1, 2, 3, 4 and 8 bits

Raising complexity with


Raising complexity with increasing q

Comparison to trellis-based decoding

� Comparison to [Park00]• Bit-clock trellis with length constraints

� Chase-like decoding• q = 3 bits

(the same search space we use),• List-Viterbi like decoding (T list size)

i pi codeword

0 0.5 0

1 0.15 1 0 0

2 0.17 1 0 1

VLC table

• L = 100 symbols


[Park00] M. Park, and D.J. Miller, "Joint source-channel decoding for variable-length encoded data by exact and approximate MAP sequence estimation," IEEE Trans. on Communications , vol. 48, no. 1, pp.1–6, Jan. 2000.

2 0.17 1 0 1

3 0.08 1 1 0

4 0.06 1 1 1 0

5 0.04 1 1 1 1

Iterative Chase-like decoding of VLCs with FEC

� Bit reliabilities definition


� Bit reliabilities definition� The case of RSC code� The case of LDPC code

Bit reliabilities definition

Chase-like VLC decoder J most likely valid bit streams (J ≤ Q)VLC decoder J most likely valid bit streams (J ≤ Q)




J best source symbol sequences:• the source sequence corresponding

to the ML compressed bit streams


to the ML compressed bit stream

• the competitor sequences (1 ≤ j < J)js



J best source symbol sequences:• the source sequence corresponding

to the ML compressed bit streams

If a symbol is the same for all sequences, there

is a huge probability that it’s correct


to the ML compressed bit stream

• the competitor sequences (1 ≤ j < J)js

that it’s correct

is reliable if for all 0 ≤ j < J

is jii ss ˆ=ˆ


s

b

VLC



s

b

VLC


Non reliable bits: They give no additional informat ionExtrinsic value = 0.0


s

b

VLC


Reliable bits: additional information can be genera tedExtrinsic value = β

The case of RSC code

RSCCπVLC

P packetsL symbols

P/S

q bits

Chase-like VLC

AWGN

MAP

RSCC

M=4 (g = {13,17})Rcc=0.5.

πVLC P/S

π-1S/P


VLC MAPπ-1S/P

πP/S

The case of RSC code

� Simulation results• Code C3

100

Tandem scheme

q=4 Iteration 1

q=4 Iteration 23

• L = 100 symbols• q = 4 and 6 bits• P = 4 packets

• Random interleaver• β = 4.0

10-3

10-2

10-1

PE

R

q=4 Iteration 2q=4 Iteration 5

q=6 Iteration 5


2 2.5 3 3.5 4 4.5 5 5.5 610

-4

10-3

Eb/N0 (dB)

The case of LDPC code

LDPC encoder

VLCL symbols

P/SH packets K bits N bits

q bits

Chase-like VLC

AWGN

LDPC decoder

encoderVLC P/S

S/P


VLC decoderS/P

P/S


……………….c1 c2 c3 cMcM-1

………... ……..v1 v2 v3 vK vN

VLCD1 VLCDh VLCDH…... ……...



……………….c1 c2 c3 cMcM-1

………... ……..v1 v2 v3 vK vN



Step 1Step 1

LDPC decoding

ItLDPC BP iterations

LDPC decoding


Step 1.1Step 1.1

Messages from LDPC variables to checks:Messages from LDPC variables to checks:

nnmnnmn oEEIT +-+= ,,


……………….c1 c2 c3 cMcM-1

………... ……..v1 v2 v3 vK vN



Step 1Step 1

LDPC decoding


LDPC decoding


Step 1.2Step 1.2

Messages from LDPC checks to variables:Messages from LDPC checks to variables:

),)((= ∑≠'

,'1-

,nn

mnnm TggE ∏≠'

,', )sign(=)sign(nn

mnnm TE


……………….c1 c2 c3 cMcM-1

………... ……..v1 v2 v3 vK vN



Step 1Step 1

LDPC decoding


LDPC decoding


Step 1.3Step 1.3

Stop criterion:� Maximum number of iterations reached� A valid LDPC codeword is obtained

Stop criterion:� Maximum number of iterations reached� A valid LDPC codeword is obtained


……………….c1 c2 c3 cMcM-1

………... ……..v1 v2 v3 vK vN



Step 2Step 2

Chase-like VLC

decoding step

Chase-like VLC

decoding step

Step 2.1Step 2.1

Apply Chase-like decoding on the H sub sequences based on the overall information given by LDPC variable nodes

Apply Chase-like decoding on the H sub sequences based on the overall information given by LDPC variable nodes


……………….c1 c2 c3 cMcM-1

………... ……..v1 v2 v3 vK vN



Step 2Step 2

Chase-like VLC

decoding step

Chase-like VLC

decoding step

Step 2.2Step 2.2

Update the extrinsic information:

for reliable bits

for non reliable bits

Update the extrinsic information:

for reliable bits

for non reliable bits

β).ˆsign(= kk bo0=ko


……………….c1 c2 c3 cMcM-1

………... ……..v1 v2 v3 vK vN



Step 3Step 3

The algorithm repeats from step 1, until:� Maximum number of overall system iterations reached,� A valid LDPC codeword containing VLC length-valid sub sequences.

The algorithm repeats from step 1, until:� Maximum number of overall system iterations reached,� A valid LDPC codeword containing VLC length-valid sub sequences.


� Simulation results• Code C33

• L = 100 symbols• q = 4 bits

• LDPC code used in DVB-S2:

Eb/N0

(dB)3.1 3.3 3.5 3.6 3.7

β 0.05 0.1 0.2 0.3 0.5


• LDPC code used in DVB-S2:• RLDPC=0.88• K=14400• N=16200• itLDPC=100 iterations

Conclusions and future work

� Conclusions


� Conclusions� Future work

Conclusions

� Chase-like decoding efficiency in the case of joint source/

channel decodingchannel decoding

� Performance improvement in the case of VLC (also AC )

� Results are asymptotically optimal

� Low-complexity and flexible solution

� Efficiency was also validated in the case of iterat ive decoding


� Efficiency was also validated in the case of iterat ive decoding

� RSC code (1.6 dB gain)

� LDPC code (The number of erroneous source sequences divided

by 500)

Future work

� How to built the best VLC, in the Chase-like decodi ng sense, for

a given source ?a given source ?

� Application to real multimedia data compression, es pecially

image and video standards

� Study in the case of a markov source

� Efficiency of Chase-like decoding with robust sourc e coding

schemes:


schemes:

� Reversible VLCs, Arithmetic Codes with forbidden sy mbol…

� Use of lengths information as synchronization marker s…

ThanksThanks

Questions ?Amin ZRIBI Improved Joint Source/ Channel decoding of VLCspage 22

Questions ?

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Improved Joint Source/ Channel Decoding of VLCs · Amin ZRIBI Improved Joint Source/ Channel decoding of VLCs. Overview of Joint Source/ Channel ... Decoding algorithm 1. Calculate