Learning in communication systems

A method comprising:

• receiving a first receiver-training sequence of messages at a first receiver of a first module of a transmission system from a second transmitter over a channel, wherein the transmission system comprises the first module having a first transmitter and the first receiver, a second module having the second transmitter and a second receiver, and the channel, wherein the first transmitter includes a first transmitter algorithm having at least some trainable weights, the second transmitter includes a second transmitter algorithm having at least some trainable weights, the first receiver has a first receiver algorithm having at least some trainable weights, and the second receiver includes a second receiver algorithm having at least some trainable weights;
• obtaining or generating a first receiver loss function, the first receiver loss function being generated based on the first receiver-training sequence as received at the first receiver and knowledge of the first receiver-training sequence as transmitted by the second transmitter;
• training at least some weights of the first receiver training algorithm based on the first receiver loss function;
• transmitting a second receiver-training sequence of messages from the first transmitter to the second receiver over the channel to enable at least some weights of the second receiver algorithm to be trained on the basis of a second receiver loss function generated based on the second receiver-training sequence as received at the second receiver and knowledge of the second receiver-training sequence as transmitted by the first transmitter;
• transmitting a perturbed version of a first transmitter-training sequence of messages from the first transmitter to the second receiver over the channel;
• receiving a first transmitter loss function at the first receiver as sent from the second transmitter over the channel, wherein the first transmitter loss function is based on the transmitted perturbed versions of the first transmitter-training sequence of messages as received at the second receiver and knowledge of the first transmitter-training sequence of messages;
• and
• training at least some weights of the transmitter algorithm of the first transmitter based on the first transmitter loss function.

A non-transitory computer readable medium storing a computer program comprising instructions, which when executed by a processor, cause an apparatus including the processor to perform the following:

• receive a first receiver-training sequence of messages at a first receiver of a first module of a transmission system from a second transmitter over a channel, wherein the transmission system comprises the first module having a first transmitter and the first receiver, a second module having the second transmitter and a second receiver, and the channel, wherein the first transmitter includes a first transmitter algorithm having at least some trainable weights, the second transmitter includes a second transmitter algorithm having at least some trainable weights, the first receiver has a first receiver algorithm having at least some trainable weights, and the second receiver includes a second receiver algorithm having at least some trainable weights;
• obtain or generate a first receiver loss function, the first receiver loss function being generated based on the first receiver-training sequence as received at the first receiver and knowledge of the first receiver-training sequence as transmitted by the second transmitter;
• train at least some weights of the first receiver training algorithm based on the first receiver loss function;
• transmit a second receiver-training sequence of messages from the first transmitter to the second receiver over the channel to enable at least some weights of the second receiver algorithm to be trained on the basis of a second receiver loss function generated based on the second receiver-training sequence as received at the second receiver and knowledge of the second receiver-training sequence as transmitted by the first transmitter;
• transmit a perturbed version of a first transmitter-training sequence of messages from the first transmitter to the second receiver over the channel;
• receive a first transmitter loss function at the first receiver as sent from the second transmitter over the channel, wherein the first transmitter loss function is based on the transmitted perturbed versions of the first transmitter-training sequence of messages as received at the second receiver and knowledge of the first transmitter-training sequence of messages;
• and
• train at least some weights of the transmitter algorithm of the first transmitter based on the first transmitter loss function.