A method and an apparatus for decoding polar codes, the method comprising: determining a starting level for processing an overflow according to a number of encoded bits of a received polar encoded codeword, an input bit-width, and an internal bit-width of a decoder; multiplying an output Log-Likelihood Ratio (LLR) value and two input LLR values of the G function by a first coefficient and a second coefficient respectively; and finally, the LLR values corresponding to the received codeword are decoded to obtain decoded bits.

A polar decoder circuit can execute successive cancellation list polar decoding on multiple threads concurrently. An LLR update engine of the polar decoder circuit and a sort engine of the polar decoder circuit can operate concurrently, with the LLR update engine computing updated path metrics for one codeword while the sort engine sorts candidates for one or more other codewords according to path metrics already computed by the LLR update engine. Threads corresponding to different codewords can cycle sequentially between the LLR update engine and the sort engine.

There is provided a method comprising, at a data receiver, receiving a channel codeword from a data sender over a noisy data channel, generating a plurality of candidate error patterns, the plurality of candidate error patterns comprising a plurality of one-bit error patterns and a plurality of multiple-bit error patterns generated from the plurality of one-bit error patterns, evaluating the plurality of candidate error patterns for codebook membership, based on the channel codeword, and outputting an estimated codeword when a codebook membership constraint is satisfied for a given candidate error pattern.

A method for determining the n best positions of frozen bits in a channel decoder for a noisy communication channel. A decoding method and decoding processing unit for implementing the channel having frozen bits at the n worst positions. A method and system that iteratively, for each bit i from the n bits, determines a probability vector for the bit i by traversing a logical graph using contraction identities simplified to specific values, indexes the specific values from the contraction identities newly computed during the determination of the probability vector for subsequent reference during a following iteration based on corresponding contraction identities, fixes the bit i from the probability vector and moving to bit i+1 until all n bits are fixed.

There is provided a method comprising, at a data receiver, receiving a channel codeword from a data sender over a noisy data channel, generating a plurality of candidate error patterns, the plurality of candidate error patterns comprising a plurality of one-bit error patterns and a plurality of multiple-bit error patterns generated from the plurality of one-bit error patterns, evaluating the plurality of candidate error patterns for codebook membership, based on the channel codeword, and outputting an estimated codeword when a codebook membership constraint is satisfied for a given candidate error pattern.

A method of dynamically changing the list size of a successive cancellation list (SCL) decoder, the SCL decoder arranged to decode data received from a wireless communications system, the method comprising at each successive cancellation stage of the SCL decoder, determining a path metric of each path of the SCL decoder, selecting a differential path metric threshold, and dynamically changing the list size of the SCL decoder based on the differential path metric threshold and the path metric of each path of the cancellation stage, such that decoding sensitivity of the decoder is maintained and/or latency and error-correction performance of the decoder are balanced.

A method for decoding a cyclic code is disclosed. The method includes: determining a plurality of syndromes for the cyclic code; determining, by a hardware processor, a first coefficient and a second coefficient based on the plurality of syndromes; determining, by the hardware processor, a third coefficient based on the second coefficient; and generating an error-locator polynomial based on the first coefficient, the second coefficient, and the third coefficient.

A method of dynamically changing the list size of a successive cancellation list (SCL) decoder, the SCL decoder arranged to decode data received from a wireless communications system, the method comprising at each successive cancellation stage of the SCL decoder, determining a path metric of each path of the SCL decoder, selecting a differential path metric threshold, and dynamically changing the list size of the SCL decoder based on the differential path metric threshold and the path metric of each path of the cancellation stage, such that decoding sensitivity of the decoder is maintained and/or latency and error-correction performance of the decoder are balanced.

A method for decoding a (n, k, d) cyclic code is disclosed. The method includes: receiving a word corresponding to the cyclic code; constructing a look-up table, wherein the look-up table includes k syndrome vectors and k error patterns; computing a syndrome vector of the received word by a hardware processor; comparing the weight of the syndrome vector of the received word with an error-correcting capacity; decoding the received word by adding the received word and the syndrome vector if the weight of the syndrome vector of the received word is not more than the error-correcting capacity; decoding the received word by inverting bits in the message section in sequence and re-compute a syndrome vector of the inverted received word if the weight of the syndrome vector of the received word is more than the error-correcting capacity.

A method for determining the n best positions of frozen bits in a channel decoder for a noisy communication channel. A decoding method and decoding processing unit for implementing the channel having frozen bits at the n worst positions. A method and system that iteratively, for each bit i from the n bits, determines a probability vector for the bit i by traversing a logical graph using contraction identities simplified to specific values, indexes the specific values from the contraction identities newly computed during the determination of the probability vector for subsequent reference during a following iteration based on corresponding contraction identities, fixes the bit i from the probability vector and moving to bit i+1 until all n bits are fixed.