In this paper, we study a cooperative coding scheme based on turbo product codes where a number of sensors transmit to a same destination with the help of a relay. This network can be modeled by a multiple-access relay channel (MARC). In the proposed scheme, the relay applies algebraic systematic Network Coding to the source codewords and forwards only the additional redundancy to the destination where an overall product codeword is observed. Based on the single-relay scenario that has been studied in a previous paper, we analyze the error probabilities at the relay input and output for different relay strategies. Taking into account the residual errors at the relay, an appropriate loglikelihood ratio is used at the destination by the turbo decoder. The error performance under the degraded source-relay channel condition is shown on the Rayleigh fading channel. Besides that, we analyze the error correlation in the relay-generated redundancy and investigate the benefits of using multi-relay cooperation. Different cooperation schemes are compared in terms of performance, complexity and energy consumption.