Turbo block codes for the binary adder channel

The Bahl-Cocke-Jelinek-Raviv Algorithm Applied to the Two-User Binary Adder Channel

“…When the β t (m) have been computed they are multiplied by the appropriate α t (m) and γ i,j (y t , m ′ , m) to obtain (18) and make decisions on (û t ,d t ). We refer the reader to [6] where some performance curves are presented for the BCJR algorithm applied to a turbo coding system for the noisy 2-BAC.…”

“…In Figure 1, consider for each user a binary rate k/n convolutional encoder, where k and n are positive integers and k < n. For simplicity we assume each encoder has overall constraint length kν and can be implemented by k shift registers, each of length ν. Let u = u ) denote the output subblocks associated with information blocks u t = (u In order to use error-correcting codes in a noisy 2-BAC and avoid the well known ambiguity resulting from the input pairs (u t = 0, d t = 1) and (u t = 1, d t = 0), a construction was proposed in [4] which employs the same error-correcting code in systematic form, for both users in Figure 1, in a serial concatenation with noiseless 2-BAC codes. However, the construction described in [4] still leads to a form of ambiguity expressed as the conditional probability equality P{u t = 0, d t = 1|y} = P{u t = 1, d t = 0|y}, which forbids the decoder of separating the symbols sent by each user in the 2-BAC at time instant t, except for the trivial cases, i.e., where u t = d t .…”

Iterative decoding of turbo convolutional codes over noisy two-user binary adder channel

“…The 2-BAC block code acts as a filter to eliminate those paths in the 2-BAC trellis [5] that would otherwise lead to ambiguity at the decoder. Further computer simulation results were presented of a construction [6] where the convolutional code employed in [4] was replaced by a turbo code [7]. Namely, the encoder for each user consists of a serial concatenation of an outer 2-BAC block code followed by a parallel concatenation of two convolutional codes as the inner code, with an interleaver between the encoders for the latter two convolutional codes.…”

Data Transmission Using Convolutional Codes and Bi-directional Soft Output Viterbi Algorithm over the Two-User Binary Adder Channel

“…In [12] the main result is a new outer bound on the zero-error capacity region that strictly improves upon the bound from Urbanke and Li [13]. A serially concatenated coding scheme is used in [14], employing a uniquely decodable pair of block codes and a pair of systematic product codes, where the decoder uses the maximum a posteriori (MAP) rule for estimating the most probable ternary sequence of a 2-BAC output. The papers [15], [16] and [17] deal with the use of the Bahl, Cocke, Jelinek and Raviv (BCJR) decoding algorithm to the 2-BAC, presenting a possibility of directly separating the binary data for each of the two users at the receiver.…”

“…As aforementioned, the MAP algorithm was adapted for the two-user case [14]- [17] and three-user case [18] in the presence of AWGN. As far as we know there is not a similar construction using a reduced complexity decoder algorithm in the published literature.…”