Decoding of a message and corresponding encoding of a message

An encoding method performed by a transmitter for encoding data of a message M to be transmitted to a receiver, the encoding method comprising:

• splitting said message M into a pre-defined number n of sub-messages M1 to Mn;
• forming data packets by means of a linear combination of said sub-messages M1 to Mn according to:
• P1=C11*M1
• P2=C21*M1+C22*M2
• . . . = . . .
• Pn=Cn1*M1+Cn2*M2+Cn3*M3+ . . . +Cnn*Mn,
• where Pn is an n-th data packet, C is an encoding matrix with element Cij at position (i,j) and Mn is an n-th sub-message of said message M;
• and
• transmitting the formed data packets to the receiver, wherein the receiver sequentially decodes said sub-messages M1 to Mn from the formed data packets with an arrival of the formed data packets, wherein the sequential decoding is performed until a decoding of a sub-message from the formed data packets is unsuccessful, wherein the sequential decoding allows the receiver to perform a significant portion of calculations associated with the decoding of said sub-messages M1 to Mn already at a reception of the formed data packets, wherein the receiver receives all remaining formed data packets when the decoding, of said sub-message from the received data packets, is unsuccessful, and wherein the receiver further decodes, all remaining sub-messages from said all remaining formed data packets, in response to a determination that said all remaining formed data packets have been received, thereby reducing a delay in the decoding of said sub-messages M1 to Mn from the formed data packets.

A receiver for decoding data from a message M receivable from a transmitter, wherein the receiver is configured to use a decoding matrix C in the decoding, and wherein said message M is split into a pre-defined number n of sub-messages M1 to Mn, the receiver comprising:

• a receiving circuit configured to receive data packets from the transmitter, wherein the received data packets are formed by a linear combination of said sub-messages M1 to Mn according to:
• P1=C11*M1
• P2=C21*M1+C22*M2
• . . . = . . .
• Pn=Cn1*M1+Cn2*M2+Cn3*M3+ . . . +Cnn*Mn,
• where Pn is an n-th data packet, C is the decoding matrix with element Cij at position (i,j) and Mn is an n-th sub-message of said message M;
• and
• a processing circuit configured to decode said sub-messages M1 to Mn from the received data packets until a decoding of a sub-message from the received data packets is unsuccessful, wherein the decoding of said sub-messages M1 to Mn is performed according to:
• M1=C11^(−1)*P1
• M2=C22^(−1)*(P2−C21*M1)
• . . . = . . .
• Mn=Cnn^(−1)*(Pn−C(N−1)*M(N−1)− . . . −C(1)*M(1))
• as the data packets are received, wherein the processing circuit is configured to decode said sub-messages M1 to Mn from the received data packets sequentially with an arrival of the data packets, wherein the sequential decoding of said sub-messages M1 to Mn with the arrival of the data packets allows performing a significant portion of calculations associated with the decoding of said sub-messages M1 to Mn already at the reception of the data packets, wherein the receiving circuit is further configured to receive all remaining data packets when the decoding, of said sub-message from the received data packets, is unsuccessful;
• and the processing circuit is further configured to decode, all remaining sub-messages from said all remaining data packets, in response to a determination that said all remaining data packets have been received, thereby reducing a delay in the decoding of said sub-messages M1 to Mn from the received data packets.

A transmitter for encoding data of a message M to be transmitted to a receiver, the transmitter comprising:

• a processing circuit configured to split said message M into a pre-defined number n of sub-messages M1 to Mn, and to form data packets by means of a linear combination of said sub-messages M1 to Mn according to:
• P1=C11*M1
• P2=C21*M1+C22*M2
• . . . = . . .
• Pn=Cn1*M1+Cn2*M2+Cn3*M3+ . . . +Cnn*Mn,
• where Pn is an n-th data packet, C is an encoding matrix with element Cij at position (i,j) and Mn is an n-th sub-message of said message M;
• and
• a transmitting circuit configured to transmit the formed data packets to the receiver, wherein the receiver sequentially decodes said sub-messages M1 to Mn from the formed data packets with an arrival of the formed data packets, wherein the sequential decoding is performed until a decoding of a sub-message from the formed data packets is unsuccessful, wherein the sequential decoding allows the receiver to perform a significant portion of calculations associated with the decoding of said sub-messages M1 to Mn already at a reception of the formed data packets, wherein the receiver receives all remaining formed data packets when the decoding, of said sub-message from the formed data packets, is unsuccessful, and wherein the receiver further decodes, all remaining sub-messages from said all remaining formed data packets, in response to a determination that said all remaining formed data packets have been received, thereby reducing a delay in the decoding of said sub-messages M1 to Mn from the formed data packets.

A system comprising:

• a transmitter configured to encode data of a message M, wherein the transmitter comprises:
• a processing circuit configured to split said message M into a pre-defined number n of sub-messages M1 to Mn, and to form data packets by means of a linear combination of said sub-messages M1 to Mn according to:
• P1=C11*M1
• P2=C21*M1+C22*M2
• . . . = . . .
• Pn=Cn1*M1+Cn2*M2+Cn3*M3+ . . . +Cnn*Mn,
• where Pn is an n-th data packet, C is an encoding matrix with element Cij at position (i,j) and Mn is an n-th sub-message of said message M, and
• a transmitting circuit configured to transmit the formed data packets;
• and
• a receiver configured to use a decoding matrix in decoding said sub-messages M1 to Mn from the formed data packets, wherein the receiver comprises:
• a receiving circuit configured to receive the formed data packets from the transmitter, and
• a processing circuit configured to decode said sub-messages M1 to Mn from the received formed data packets until a decoding of a sub-message from the received formed data packets is unsuccessful, wherein the decoding of said sub-messages M1 to Mn is performed according to:
• M1=C11^(−1)*P1
• M2=C22^(−1)*(P2−C21*M1)
• . . . = . . .
• Mn=Cnn^(−1)*(Pn−C(N−1)*M(N−1)− . . . −C(1)*M(1))
• as the formed data packets are received, wherein the processing circuit is configured to decode said sub-messages M1 to Mn from the received formed data packets sequentially with an arrival of the received formed data packets, wherein the sequential decoding of said sub-messages M1 to Mn with the arrival of the received formed data packets allows performing a significant portion of calculations associated with the decoding of said sub-messages M1 to Mn already at the reception of the data packets, wherein the receiving circuit is further configured to receive all remaining formed data packets when the decoding, of said sub-message from the received data packets, is unsuccessful, and wherein the processing circuit is further configured to decode, all remaining sub-messages from said all remaining formed data packets, in response to a determination that said all remaining formed data packets have been received, thereby reducing a delay in the decoding of said sub-messages M1 to Mn from the received formed data packets.