Abstract
The Bahl-Cocke-Jelinek-Raviv (BCJR) algorithm is a well known maximum a posteriori probability decoding algorithm which has been proposed earlier for point to point communication applications, employing block codes or convolutional codes, and turbo codes. This paper describes an application of the BCJR algorithm for decoding the output of a multiple access channel called the noisy two-user binary adder channel, in the presence of additive white Gaussian noise.
Highlights
T HE Bahl-Cocke-Jelinek-Raviv (BCJR) algorithm [1] is a well known maximum a posteriori probability decoding algorithm which has been proposed for point to point communication applications, employing block codes or convolutional codes [1], and turbo codes [2]
In this paper we apply the BCJR decoding algorithm to the two-user communication system illustrated in Figure 1, where the channel is the twouser binary adder channel (2-BAC) [3] with the addition of noise
In the noiseless case the 2-BAC output yt, at time t, is just the arithmetic sum of the binary inputs vt and wt, i.e., yt = vt + wt ∈ {−2, 0, 2}, while in the noisy case yt = vt +wt+qt and the noisy 2-BAC output behaviour is described by the conditional probability P, where qt denotes a sample of a time-discrete noise process which here we assume to be additive white Gaussian noise (AWGN)
Summary
T HE Bahl-Cocke-Jelinek-Raviv (BCJR) algorithm [1] is a well known maximum a posteriori probability decoding algorithm which has been proposed for point to point communication applications, employing block codes or convolutional codes [1], and turbo codes [2]. The construction described in [4] still leads to a form of ambiguity expressed as the conditional probability equality P{ut = 0, dt = 1|y} = P{ut = 1, dt = 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 ut = dt. For this reason we consider always distinct turbo codes for user 1 and user 2, respectively. The use of distinct codes allows both the correction of errors due to noise and the correction of errors due to the interference between users
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