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