In this paper, we propose a new distributed coding structure with a soft input soft output (SISO) relay encoder for error-prone parallel relay channels. We refer to it as the distributed soft coding (DISC). In the proposed scheme, each relay first uses the received noisy signals to calculate the soft bit estimate (SBE) of the source symbols. A simple SISO encoder is developed to encode the SBEs of source symbols based on a constituent code generator matrix. The SISO encoder outputs at different relays are then forwarded to the destination and form a distributed codeword. The performance of the proposed scheme is analyzed. It is shown that its performance is determined by the generator sequence weight (GSW) of the relay constituent codes, where the GSW of a constituent code is defined as the number of ones in its generator sequence. A new coding design criterion for optimally assigning the constituent codes to all the relays is proposed based on the analysis. Results show that the proposed DISC can effectively circumvent the error propagation due to the decoding errors in the conventional detect and forward (DF) with relay re-encoding and bring considerable coding gains, compared to the conventional soft information relaying.

In a wireless multi-hop relay network, the optimal routing scheme with exhaustive path search entails high computational complexity and large storage requirement, and is impractical for a large number of hops. In this paper, we propose a suboptimal path selection scheme, based on amplify-and-forward (AF) protocol, that has outage performance close to the optimal routing scheme, but with much less complexity. The proposed scheme draws on the analogy between the node distribution of a commonly used relay network model and the trellis of a convolutional code, and applies the Viterbi algorithm in selecting a path to maximize the end-to-end signal-to-noise ratio (SNR). In specific, the relay network topology is first mapped to the trellis diagram of a convolutional code. In the trellis, the branch metric is defined as the inverse of the instantaneous SNR of the channel connecting two relays in two adjacent clusters. Consequently, the path metric is equal to the inverse of the equivalent SNR of the path. Then, the sliding window Viterbi algorithm is used to select a path from the source to the destination. Simulation results show that when the window size is five times the total encoder memory or more, the proposed routing scheme achieves near optimal outage performance. The proposed scheme has a polynomial complexity and low communication overhead. Therefore, it is very efficient for relay networks with a large number of hops.

In this paper, we revisit the BCJR soft-input soft-output (SISO) maximum a posteriori probability (MAP) decoding process of rate-1 recursive convolutional (RC) codes. From this we establish some interesting duality properties between encoding and decoding of RC codes. We observe that the forward and backward BCJR decoders can be simply represented by their dual SISO channel encoders using shift registers in the complex field. Similarly, the bidirectional MAP decoding can be implemented by linearly combining the outputs of the dual SISO encoders of the respective forward and backward decoders.

Distributed coding has been shown to be an efficient scheme to improve the performance of wireless relay networks. In this paper we propose an analog distributed channel coding (ADC) scheme. In the proposed scheme, the intermediate relays directly process the received analog noisy signals without making the hard estimation and performs analog channel encoding of the noisy soft estimates of the transmitted symbols, so that the processed signals forwarded by all relays can form an analog distributed convolutional codeword. Assuming the source packet is encoded by a channel code, the ADC scheme can form serial concatenated codes and iterative decoding can be applied at the destination. We compare our proposed scheme with other existing schemes under Additive White Gaussian Noise (AWGN) and fast Rayleigh fading channel and validate the simulation results with the aid of Extrinsic Information Transfer (EXIT) chart analysis. Simulation results show that the proposed ADC scheme can effectively overcome the error propagation due to the erroneous decoding at the relay in the conventional decode-forward (DF) scheme and provide considerable coding gains, thus considerably outperforming the conventional soft information relaying protocols. The coding gains increase as the number of state in the relay encoder increases.