Abstract: A method for decoding polar codes based encoded data comprises receiving the polar codes based encoded data, determining a rate at which the data is encoded, based on the determined rate, selecting suitable implemented super nodes in a flexible-rate polar decoder, and decoding the polar codes based encoded data. A receiver in a communication system, including a flexible-rate polar decoder; and a controller configured to: receive the polar codes based encoded data; determine a rate at which the data is encoded; based on the determined rate, select suitable implemented super nodes in a flexible-rate polar decoder; and decode the polar codes based encoded data.

Abstract: A method for decoding polar codes based encoded data comprises receiving the polar codes based encoded data, determining a rate at which the data is encoded, based on the determined rate, selecting suitable implemented super nodes in a flexible-rate polar decoder, and decoding the polar codes based encoded data. A flexible-rate polar decoder is created by receiving polar codes corresponding to a set of desired overheads, generating, for each overhead, a binary tree using fast successive cancellation decoding, generating a unified binary tree by determining locations of super nodes within each binary tree, representing the determined locations having same node index among different binary trees as super locations in the unified binary tree, each super location including more than one super node, and implementing the unified binary tree on an application specific hardware structure to create the flexible-rate polar decoder.

Abstract: An application-specific hardware device and methods for decoding data and methods are disclosed. The data includes a plurality of encoded non-binary data symbols, the application-specific hardware device receives the plurality of encoded non-binary data symbols, each encoded non-binary data symbol being received through a corresponding channel, determines, for each encoded non-binary data symbol, a log-likelihood ratio vector, applies a successive cancellation decoding routine to the plurality of log-likelihood ratio vectors, the successive cancellation decoding routine comprising one or more groups of operations to be applied to subsets of the plurality of log-likelihood ratio vectors and generates a plurality of decoded non-binary data symbols based on a result of the successive cancellation decoding routine.

Abstract: An application-specific hardware device and methods for decoding data and methods are disclosed. The data includes a plurality of encoded non-binary data symbols, the application-specific hardware device receives the plurality of encoded non-binary data symbols, each encoded non-binary data symbol being received through a corresponding channel, determines, for each encoded non-binary data symbol, a log-likelihood ratio vector, applies a successive cancellation decoding routine to the plurality of log-likelihood ratio vectors, the successive cancellation decoding routine comprising one or more groups of operations to be applied to subsets of the plurality of log-likelihood ratio vectors and generates a plurality of decoded non-binary data symbols based on a result of the successive cancellation decoding routine.

Abstract: Disclosed are systems and methods for transmission and reception of data bits. A plurality of data bits are received. FEC-based encoded data bits are generated in accordance with a zipper code framework incorporating component non-binary codes. The zipper code framework includes a buffer having a virtual buffer and a real buffer. Codewords associated with the FEC-based encoded data bits are stored in rows of the real buffer. A given codeword in a given row of the real buffer is mapped to different rows of the virtual buffer in a quasi-diagonal interleaving manner.

Abstract: Forward Error Correction decoding is executed by acquiring a stream of real data symbols from a communication medium, the stream of real data symbols being arranged in a real matrix. Virtual data symbols are generated and arranged in a virtual matrix by applying an interleaver map onto the real matrix. Codewords formed by a main matrix formed by the real matrix and the virtual matrix are iteratively decoded, an iteration of the decoding comprising identifying a set of consecutive received rows of the main matrix, accessing a set of pre-determined reference codewords and in response to determining that a given codeword of the set of consecutive received rows does not match any pre-determined reference codewords, executing a GRAND algorithm on the given codeword, the GRAND algorithm generating a substitute codeword for the given codeword. A system comprising a processor and a memory executes the Forward Error Correction decoding.

Abstract: Forward Error Correction decoding is executed by acquiring a stream of real data symbols from a communication medium, the stream of real data symbols being arranged in a real matrix. Virtual data symbols are generated and arranged in a virtual matrix by applying an interleaver map onto the real matrix. Codewords formed by a main matrix formed by the real matrix and the virtual matrix are iteratively decoded, an iteration of the decoding comprising identifying a set of consecutive received rows of the main matrix, accessing a set of pre-determined reference codewords and in response to determining that a given codeword of the set of consecutive received rows does not match any pre-determined reference codewords, executing a GRAND algorithm on the given codeword, the GRAND algorithm generating a substitute codeword for the given codeword. A system comprising a processor and a memory executes the Forward Error Correction decoding.

Abstract: The disclosed systems, structures, and methods are directed to encoding and decoding information for transmission across a communication channel. The encoding method includes: distributing the information bits between m parallel polar codes such that each of the m parallel polar codes includes a subset of the information bits; splitting the subset of information bits in each of the m parallel polar codes into a protected information section and a full rate information section; protecting information bits in the protected information section of each of the m parallel polar codes; arranging a plurality of frozen bits in each of the m parallel polar codes; and generating a polar encoded codeword for each of the m parallel polar codes.

Abstract: The disclosed systems and methods for transmission and reception comprising: i) receiving a plurality of data bits; ii) generating FEC-based encoded data bits in accordance with a zipper code framework incorporating component non-binary codes, wherein the zipper code framework including a buffer having a virtual buffer and a real buffer; iii) storing codewords associated with the FEC-based encoded bits in rows of the real buffer; iv) mapping a given codeword in a given row of the real buffer to different rows of the virtual buffer; v) receiving an analog signal transmitted by a transmitter; vi) processing the received analog signal and generating received forward error correction (FEC)-based encoded bits in accordance with a zipper code framework that incorporates component non-binary codes; and vii) decoding the received FEC-based encoded bits in accordance with a non-binary decoding technique and generating information bits.

Abstract: The disclosed hybrid product polar codes-based communication systems and methods for i) receiving a stream of information bits; ii) reshaping the stream of information bits into at least a first rectangular information matrix M1 of size Kr1×Kc1 and a second rectangular information matrix M2 of size Kr2×Kc2; iii) converting the rectangular information matrices M1 and M2 to 2D product polar code encoded matrices X1 and X2 respectively using product polar codes, the 2D product polar code encoded matrices X1 and X2 having a size of Nr1×Nc1 and Nr2×Nc2 respectively; iv) converting the 2D product polar code encoded matrices X1 and X2 to a stream of encoded bits X?; and v) encoding the stream of encoded bits X? to a stream of polar encoded bits X? using the polar codes.

Abstract: An optical transmitter device includes a digital signal processor (DSP) having digital hardware. The DSP is operative to generate shaped bits from a first set of information bits, and to apply a systematic forward error correction (FEC) scheme to encode the shaped bits and a second set of information bits, where the first set of information bits and the second set of information bits are disjoint sets. Unshaped bits and the shaped bits are mapped to selected symbols or are used to select symbols from one or more constellations. The selected symbols are mapped to physical dimensions. Each unshaped bit is either one of the second set of information bits or one of multiple parity bits resulting from the FEC encoding. In this manner, a target spectral efficiency is achieved.

Abstract: A polar encoder comprises an input, an output and a processor operatively connected to the input and to the output. The input either receives first, second and third codewords, or receives information bits used by the processor for generating first, second and third probabilistic constellation shaping codewords. The processor combines the first and second codewords, to produce a first modulation symbol bit, combines the first and third codewords to produce a second modulation symbol bit, and combines the first, second and third codewords to produce a third modulation symbol bit. The output forwards the modulation symbol bits to a bit to symbol mapper. The polar encoder may be included in a transmitter that further comprises the bit to symbol mapper receiving the modulation symbol bits and generating modulation symbols, and a modulator modulating a carrier using the modulation symbols.

Abstract: An optical transmitter device (14) includes a digital signal processor ‘DSP’ (20) having digital hardware (30). The DSP is operative to generate (102,202,302) shaped bits from a first set of information bits, and to apply (104,204,304) a systematic forward error correction ‘FEC’ scheme to encode the shaped bits and a second set of information bits, where the first set of information bits and the second set of information bits are disjoint sets. Unshaped bits and the shaped bits are mapped to selected symbols or are used to select symbols from one or more constellations. The selected symbols are mapped to physical dimensions. Each unshaped bit is either one of the second set of information bits or one of multiple parity bits resulting from the FEC encoding. In this manner, a target spectral efficiency is achieved.

Abstract: Methods and encoders for encoding information bits to generate codewords for transmission across a communication channel are described. The method includes receiving input data comprising bits of information bits and frozen bits. Each bit has a value. Further, the method identifies at least one special arrangement in a subset of input data depending on locations of the information bits and the frozen bits. This subset of input data is of length L. The subset of input data has at least one special arrangement that enables direct computations instead of a series of computations to determine a preliminary output. The method generates a codeword for the input data from the preliminary output.

Abstract: A polar encoder comprises an input, an output and a processor operatively connected to the input and to the output. The input either receives first, second and third codewords, or receives information bits used by the processor for generating first, second and third probabilistic constellation shaping codewords. The processor combines the first and second codewords, to produce a first modulation symbol bit, combines the first and third codewords to produce a second modulation symbol bit, and combines the first, second and third codewords to produce a third modulation symbol bit. The output forwards the modulation symbol bits to a bit to symbol mapper. The polar encoder may be included in a transmitter that further comprises the bit to symbol mapper receiving the modulation symbol bits and generating modulation symbols, and a modulator modulating a carrier using the modulation symbols.

Abstract: Methods and encoders for encoding information bits to generate codewords for transmission across a communication channel are described. The method includes receiving input data comprising bits of information bits and frozen bits. Each bit has a value. Further, the method identifies at least one special arrangement in a subset of input data depending on locations of the information bits and the frozen bits. This subset of input data is of length L. The subset of input data has at least one special arrangement that enables direct computations instead of a series of computations to determine a preliminary output. The method generates a codeword for the input data from the preliminary output.

Abstract: The disclosed systems, structures, and methods are directed to encoding and decoding information for transmission across a communication channel. The encoding method includes: distributing the information bits between m parallel polar codes such that each of the m parallel polar codes includes a subset of the information bits; splitting the subset of information bits in each of the m parallel polar codes into a protected information section and a full rate information section; protecting information bits in the protected information section of each of the m parallel polar codes; arranging a plurality of frozen bits in each of the m parallel polar codes; and generating a polar encoded codeword for each of the m parallel polar codes.

Abstract: The disclosed systems and methods for encoding, by a polar encoder, K message bits into an encoded message bits sequence C(M) using polar codes, where K and M are integer values and M is greater than or equal to K; rearranging, by an interleaver, the encoded message bits sequence C(M) to rearranged encoded message bits sequence C?(M) such that a C(i)th bit and a C ? ( M 2 + i ) th bit of the encoded message bits sequence C(M) are arranged together, where i is an integer value that varies between 1 to M 2 ; mapping, by a bits-to-symbol mapper, the rearranged encoded message bits sequence C(M) to N non-binary symbols, where N is an integer value; and processing, by a transmitter symbol processor, the N non-binary symbols to transmit the processed non-binary symbols towards a receiver.

Abstract: The disclosed systems, structures, and methods are directed to encoding and decoding information for transmission across a communication channel. The encoding method includes: distributing the information bits between m parallel polar codes such that each of the m parallel polar codes includes a subset of the information bits; splitting the subset of information bits in each of the m parallel polar codes into a protected information section and a full rate information section; protecting information bits in the protected information section of each of the m parallel polar codes; arranging a plurality of frozen bits in each of the m parallel polar codes; and generating a polar encoded codeword for each of the m parallel polar codes.

Abstract: The disclosed systems, structures, and methods are directed to encoding and decoding information for transmission across a communication channel. The encoding method includes: distributing the information bits between m parallel polar codes such that each of the m parallel polar codes includes a subset of the information bits; splitting the subset of information bits in each of the m parallel polar codes into a protected information section and a full rate information section; protecting information bits in the protected information section of each of the m parallel polar codes; arranging a plurality of frozen bits in each of the m parallel polar codes; and generating a polar encoded codeword for each of the m parallel polar codes.