In this paper, we consider multichannel ALOHA for a wireless sensor network (WSN), where sensors' signals are correlated. The impact of the number of channels on the length of information that an access point (AP) can collect is investigated. Under a certain distributed signal source model, in order for the AP to have a sufficiently long length of information, we show that the number of channels is to be larger than the square of the average number of active nodes. Thus, when the number of channels is limited, we need to use re-transmissions. To this end, we propose an adaptive transmission approach that can effectively exploit the correlation between the collected signals at the AP and nodes' signals using Slepian-Wolf coding to shorten the total transmission time, which results in a more energy efficient WSN.