Let x n be the digital signal that results from the quantization of x ~ n with a fixed-rate uniform quantizer of B bits/sample and step size: Δ = A max - A min / 2 B. The easiest way of reducing the bit rate of x ~ n is to remove the l-least significant bits (LSBs) of each codeword of x ~ n.
Here, log is taken to base 2, ρ denotes the transmit signal-to-noise ratio (SNR), where we have assumed that all transmitters are under the same and fixed power constraint, |·| denotes the Euclidean norm of a vector, and R ~ denotes the number of bits in each codeword transmitted by sourcesa.
The decoder is fully block-parallel, with all bits of each 256-bit codeword being processed by 256 variable nodes and 128 parity check nodes that together form an 8-stage iteration pipeline.
The N bits of a codeword are represented in the systematic form, divided in information bits (IN) and parity-check bits (PN) given by the number of columns of A and B, respectively.
Finally, conclusions are drawn in Section 9. LDPC codes are linear block-codes described by a parity-check matrix establishing a certain number of (even) parity constraints on the bits of a codeword.
where r1, r2, …, r3 are the soft-decision bits of the codeword C r, {hk,u|1 ≤ k ≤ n r, 1 ≤ u ≤ l} are the elements of Hbmin(m λ (x)) in GF(2).
The adaptive processing for a given received codeword C r and a binary minimal parity-check matrix Hbmin(m λ (x)) includes the following steps: 1) Combine Hb min(m λ (x)) and C r T to form a matrix H * (m λ (x)) as follows: (28) where r1, r2, …, r3 are the soft-decision bits of the codeword C r, {hk,u|1 ≤ k ≤ n r, 1 ≤ u ≤ l} are the elements of Hbmin(m λ (x)) in GF(2).
In [9], the length of each codeword being transmitted in BC and MAC modes is 1,296 bits and the rate is 1/2.
The K information bits of each source are encoded via point-to-point channel codes into a systematic codeword, denoted as source codeword, of length L, expressed by the column vector s u s for user u s, u s ∈ [1,…,m s ].
If the channels are correctly equalized, we may assume that the LLRs of all bits of the FEC codeword are extracted from the same equivalent channel, with SNRs expressed by (1) for the algorithm which employ the source-destination link, respectively, by (2) for topologies which do not employ this link.
