January 18, 2015

Inactivation Decoding of LT CodesFrancisco Lázaro Blasco

Institute for Communications and NavigationGerman Aerospace Center, DLR

Page 0/2 F. Lázaro ⋅ Fountain Codes ⋅ January 18, 2015

Digital Fountain

• The encoder acts like a fountain▸ Each water drop is a packet▸ Receiver: after receiving enough drops the glass if full and

decoding is successful

Page 1/2 F. Lázaro ⋅ Fountain Codes ⋅ January 18, 2015

Fountain codes

• Fountain Codes are rateless erasure codes• Encoding

▸ k input symbols▸ l output symbols, where l = k ,⋯,∞▸ rate r = k

l

• Decoding▸ decoding is possible when m = k + δ symbols are received▸ δ small

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Motivation

• Most works on LT codes assume:▸ Very long block sizes (k >> 10 000)▸ Belief Propagation (BP) decoding

• In practice:▸ moderate block sizes (k ≤ 8192 in [1], [2])▸ efficient ML decoding (inactivation decoding) is used

instead of BP

• How do we design finite length Fountain codes forinactivation decoding?

[1] 3GPP TS 26.346 V11.1.0: Technical Specification Group Services and System Aspects; MultimediaBroadcast/Multicast Service; Protocols and Codecs June 2012

[2] RFC 5053: Network working group; Request for Comments: 5053; Raptor Forward Error Correction Scheme forObject Delivery Oct. 2007