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Concatenated Irregular Variable Length Coding and Irregular Unity Rate Coding R. G. Maunder and L. Hanzo Communications Research Group School of Electronics and Computer Science, University of Southampton, SO17 1BJ, UK.

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School of ECS, Univ. of Southampton, UK. http://www-mobile.ecs.soton.ac.uk 1/ 14 ⇒ |

Concatenated Irregular Variable Length Coding and Irregular Unity Rate Coding

R. G. Maunder and L. Hanzo

Communications Research Group School of Electronics and Computer Science, University of Southampton, SO17 1BJ, UK. http://www-mobile.ecs.soton.ac.uk

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School of ECS, Univ. of Southampton, UK. http://www-mobile.ecs.soton.ac.uk 2/ 14 ⇒ |

Outline

❏ Serial concatenations of regular and irregular codes ❏ EXIT chart matching ❏ BER and complexity performance results ❏ Summary

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Concatenation of regular codes

VLC encoder π−1 π π c d b a VLC decoder URC decoder ˆ a ˜ d ˜ ce ˜ ca ˜ be ˜ ba URC encoder

VLC-URC η = 2.12 Eb/N0 = 5.97 dB I(˜ ca; c), I(˜ be; b) I(˜ ce; c), I(˜ ba; b) 1 0.8 0.6 0.4 0.2 1 0.8 0.6 0.4 0.2

105 bits 106 bits Eb/N0 = 4.57 dB Eb/N0 = 4.28 dB VLC-URC η = 2.12 Eb/N0 [dB] BER 7 6 5 4 100 10−1 10−2 10−3 10−4 10−5

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Concatenation of irregular and regular codes

N VLC encoders π−1 π π c d b1 bN b a1 aN a N VLC decoders URC decoder ˜ ba

˜ ba

˜ be

ˆ a1 ˆ aN ˆ a ˜ d ˜ ce ˜ ca ˜ be ˜ ba URC encoder

IrVLC-URC η = 2.12 Eb/N0 = 5.11 dB I(˜ ca; c), I(˜ be; b) I(˜ ce; c), I(˜ ba; b) 1 0.8 0.6 0.4 0.2 1 0.8 0.6 0.4 0.2

105 bits 106 bits Eb/N0 = 4.57 dB Eb/N0 = 4.28 dB IrVLC-URC η = 2.12 Eb/N0 [dB] BER 7 6 5 4 100 10−1 10−2 10−3 10−4 10−5

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Concatenation of irregular codes

N VLC encoders M URC encoders π−1 π π c1 c cM d1 dM d b1 bN b a1 aN a N VLC decoders M URC decoders ˜ ba

˜ ba

˜ be

ˆ a1 ˆ aN ˆ a ˜ d1 ˜ dM ˜ ce

˜ ce

˜ ca

˜ d ˜ ce ˜ ca ˜ be ˜ ba

IrVLC-IrURC η = 2.12 Eb/N0 = 4.61 dB I(˜ ca; c), I(˜ be; b) I(˜ ce; c), I(˜ ba; b) 1 0.8 0.6 0.4 0.2 1 0.8 0.6 0.4 0.2

105 bits 106 bits Eb/N0 = 4.57 dB Eb/N0 = 4.28 dB IrVLC-IrURC η = 2.12 Eb/N0 [dB] BER 7 6 5 4 100 10−1 10−2 10−3 10−4 10−5

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GA for designing component VLC codebooks

❏ Arbitrary EXIT curve ❏ Near-unity VLC-encoded bit entropy ❏ Low decoding complexity

N = 30 I(˜ be

n; bn)

I(˜ ba

n; bn)

1 0.8 0.6 0.4 0.2 1 0.8 0.6 0.4 0.2

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Full search for selecting component URC codes

M = 10, Eb/N0 = 4.74 dB I(˜ ca

m; cm)

I(˜ ce

m; cm)

1 0.8 0.6 0.4 0.2 1 0.8 0.6 0.4 0.2

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EXIT chart matching

I(˜ xe; x) = fx [I(˜ xa; x)] IrVLC EXIT function... fb = N

n=1 αnfbn,

where N

n=1 αn = 1,

αn ≥ 0 ∀ n ∈ [1 . . . N], R = N

n=1 αnRn.

IrURC EXIT function... fc = M

m=1 αmfcm,

where M

m=1 αm = 1,

αm ≥ 0 ∀ m ∈ [1 . . . M].

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Joint EXIT chart matching algorithm

EXIT N VLC functions coding rate incremental Match with IrURC EXIT function IrVLC EXIT function Match EXIT M URC functions EXIT 1 URC function

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EXIT chart matching accuracy

VLC-URC IrVLC-URC IrVLC-IrURC Attainable capacity Channel capacity η = 2.12 Eb/N0 [dB] η = 4R 14 12 10 8 6 4 2 4 3.5 3 2.5 2 1.5 1

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EXIT charts

VLC-URC η = 2.12 Eb/N0 = 5.97 dB I(˜ ca; c), I(˜ be; b) I(˜ ce; c), I(˜ ba; b) 1 0.8 0.6 0.4 0.2 1 0.8 0.6 0.4 0.2 IrVLC-URC η = 2.12 Eb/N0 = 5.11 dB I(˜ ca; c), I(˜ be; b) I(˜ ce; c), I(˜ ba; b) 1 0.8 0.6 0.4 0.2 1 0.8 0.6 0.4 0.2 IrVLC-IrURC η = 2.12 Eb/N0 = 4.61 dB I(˜ ca; c), I(˜ be; b) I(˜ ce; c), I(˜ ba; b) 1 0.8 0.6 0.4 0.2 1 0.8 0.6 0.4 0.2

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BER performance

VLC-URC 100 000 bits VLC-URC 1 000 000 bits IrVLC-URC 100 000 bits IrVLC-URC 1 000 000 bits IrVLC-IrURC 100 000 bits IrVLC-IrURC 1 000 000 bits Eb/N0 = 4.57 dB Eb/N0 = 4.28 dB Eb/N0 [dB] BER 7 6 5 100 10−1 10−2 10−3 10−4 10−5

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Decoding complexity

VLC-URC 100 000 bits VLC-URC 1 000 000 bits IrVLC-URC 100 000 bits IrVLC-URC 1 000 000 bits IrVLC-IrURC 100 000 bits IrVLC-IrURC 1 000 000 bits Eb/N0 = 4.57 dB Eb/N0 = 4.28 dB Eb/N0 [dB] Average ACS per source symbol 7 6 5 106 105 104

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