Raptor codes on binary memoryless symmetric channels

Fountain Coding with Decoder Side Information

“…For that δ, by means of linear programming (discretization of the segment), we have found the distributions Φ with minimum average degree. This method can be naturally extended to the finite length design, similarily as in [3], based on setting lower bounds on the expected size of the input ripple [11]. Table I shows four distributions calculated in this way.…”

“…This means that y = BIAW GN σV (x), where BIAWGN stands for the binary input additive white Gaussian noise channel (this is the virtual channel). Note that in this case we have H(X|Y ) = 1 − Cap (BIAW GN σV ), where the capacity of BIAWGN channel of noise variance σ 2 [3] is given by…”

“…The optimization of fountain code output degree distribution for the BIAWGN channel when soft information is not present at the input nodes was treated in [3] by using a refined Gaussian approximation [13]. This optimization is based on the simple rationale that the means of the messages transmitted from the input nodes to the output nodes should keep on increasing under the usual all-zeroes information sequence assumption.…”

“…Ω (1) is the output edge degree distribution (the proportion of incoming messages which carry the mean f d (µ)), α is the average input degree and f d (µ) is the refined mean [3] of the messages passed from the output node of degree d when the mean of the incoming messages is µ.…”

“…The first practical DF codes were Luby-Transform (LT) codes [1], whereas their extension, Raptor codes [2], represent a state-of-the-art DF solution for lossy transmission with excellent performance and linear encoding/decoding complexity. A significant amount of work has been done to extend the methods of DF codes for transmission over noisy channels [3], [4]. In this paper we consider another possible application of DF codes, which is set in the realm of distributed joint source-channel coding (DJSCC).…”