Methods and apparatus for error correction coding integrated with transmission diversity

A method performed by a transmitter apparatus in a communication system, the method comprising:

• an encoding step, wherein the encoding step comprises:
• identifying a data word d from a source;
• and
• identifying a plurality of encoder output subwords x1, x2, . . . , xr from the data word d based on an encoder input mapping relation and a plurality of encoding functions, wherein r is greater than one;
• and
• a diversity mapping step, wherein the diversity mapping step comprises:
• identifying a plurality of channel input subwords v1, v2, . . . , vs from the plurality of encoder output subwords x1, x2, . . . , xr based on a diversity transform and a subchannel assignment relation;
• and
• transmitting the plurality of channel input subwords v1, v2, . . . , vs over a channel, wherein the channel comprises a plurality of subchannels, wherein s is related to a number of subchannels and s is greater than one.

A receiver apparatus in a communication system, the receiver apparatus comprising:

• memory storing instructions;
• and
• processing circuitry coupled to the memory and configured, based at least partially on the instructions, to cause the receiver apparatus to:
• receive a plurality of channel output subwords y1, y2, . . . , ys from a channel, wherein the channel comprises a plurality of subchannels, wherein s is related to a number of subchannels and s is greater than one,
• identify an ith decoder input statistic li in an ith iteration of a receiver process, wherein the ith decoder input statistic li is based on y1, y2, . . . , ys, any decision feedback messages in iterations prior to the ith iteration, and a diversity transform matrix GDIV, wherein GDIV is a r×t matrix with t>r≥2,
• send the ith decoder input statistic li, and
• obtain an ith decision feedback message;
• and
• obtain the ith decoder input statistic li,
• identify an ith partial decoder decision based on the ith decoder input statistic li, wherein the ith partial decoder decision comprises an ith decoded encoder input subword ûi,
• determine whether an ith termination condition is satisfied,
• in case that the ith termination condition is not satisfied, identify an ith decision feedback message and send the ith decision feedback message, wherein the ith decision feedback message is based on the ith partial decoder decision and comprises an ith decoded encoder output subword {circumflex over (x)}i, wherein {circumflex over (x)}i is obtained from the ith decoded encoder input subword ûi based on an ith encoding function, wherein the ith encoding function comprises an ith encoding matrix G(i) with Mi rows and N columns, wherein Mi is a number of elements of ûi, wherein N is a number of elements of {circumflex over (x)}i, wherein 1≤Mi≤N, wherein N is the same for each {circumflex over (x)}i, 1≤i≤r,
• in case that an termination condition is satisfied, identify a decoder output and sending the decoder output to a destination, wherein the decoder output comprises a decoded data word {circumflex over (d)}, wherein {circumflex over (d)}Bi=(ûi)Di for each 1≤i≤r, wherein (B1, B2, . . . , Br) is a non-trivial partition of {1, 2, . . . , K}, wherein (D1, D2, . . . , Dr) is a collection of sets such that Di⊂{1, 2, . . . , Mi}, wherein |D_i|=B_i| for each 1≤i≤r, wherein K is a number of elements of {circumflex over (d)}, wherein K≥2.

A method performed by a receiver apparatus in a communication system, the method comprising:

• receiving a plurality of channel output subwords y1, y2, . . . , ys from a channel, wherein the channel comprises a plurality of subchannels, wherein s is related to a number of subchannels and s is greater than one, and
• identifying an ith decoder input statistic li in an ith iteration of a receiver process, wherein the ith decoder input statistic li is based on y1, y2, . . . , ys, any decision feedback messages in iterations prior to the ith iteration, and a diversity transform matrix GDIV, wherein GDIV is a r×t matrix with t>r≥2,
• sending the ith decoder input statistic li, and
• obtaining an ith decision feedback message;
• and
• obtaining the ith decoder input statistic li,
• identifying an ith partial decoder decision based on the ith decoder input statistic li, wherein the ith partial decoder decision comprises an ith decoded encoder input subword ûi,
• determining whether an ith termination condition is satisfied,
• in case that the ith termination condition is not satisfied, identifying an ith decision feedback message and sending the ith decision feedback message, wherein the ith decision feedback message is based on the ith partial decoder decision and comprises an ith decoded encoder output subword {circumflex over (x)}i, wherein {circumflex over (x)}i is obtained from the ith decoded encoder input subword ûi based on an ith encoding function, wherein the ith encoding function comprises an ith encoding matrix G(i) with Mi rows and N columns, wherein Mi is a number of elements of ûi, wherein N is a number of elements of {circumflex over (x)}i, wherein 1≤Mi≤N, wherein N is the same for each {circumflex over (x)}i, 1≤i≤r,
• in case that an termination condition is satisfied, identifying a decoder output and sending the decoder output to a destination, wherein the decoder output comprises a decoded data word {circumflex over (d)}, wherein {circumflex over (d)}B=(ûi)Di for each 1≤i≤r, wherein (B1, B2, . . . , Br) is a non-trivial partition of {1, 2, . . . , K}, wherein (D1, D2, . . . , Dr) is a collection of sets such that Di⊂{1, 2, . . . , Mi}, wherein |D_i|=B_i| for each 1≤i≤r, wherein K is a number of elements of {circumflex over (d)}, wherein K≥2.