Systems and methods for decoding block and concatenated codes are provided. These include advanced iterative decoding techniques based on belief propagation algorithms, with particular advantages when applied to codes having higher density parity check matrices such as iterative soft-input soft-output and list decoding of convolutional codes, Reed-Solomon codes and BCH codes. Improvements are also provided for performing channel state information estimation including the use of optimum filter lengths based on channel selectivity and adaptive decision-directed channel estimation. These improvements enhance the performance of various communication systems and consumer electronics. Particular improvements are also provided for decoding HD radio signals, satellite radio signals, digital audio broadcasting (DAB) signals, digital audio broadcasting plus (DAB+) signals, digital video broadcasting-handheld (DVB-H) signals, digital video broadcasting-terrestrial (DVB-T) signals, world space system signals, terrestrial-digital multimedia broadcasting (T-DMB) signals, and China mobile multimedia broadcasting (CMMB) signals. These and other improvements enhance the decoding of different digital signals.

A method of processing broadcast data in a broadcast transmitting system, the method includes randomizing, by a hardware processor, the broadcast data; first encoding, by the hardware processor, the randomized broadcast data to add first parity data for first forward error correction; second encoding, by the hardware processor, the first-encoded broadcast data to add second parity data for second forward error correction; permuting the second-encoded broadcast data; block interleaving, by the hardware processor, the permuted broadcast data; third encoding signaling information for signaling the broadcast data to add parity data; fourth encoding the third-encoded signaling information at a code rate; block interleaving the fourth-encoded signaling information; modulating the block-interleaved broadcast data and the block-interleaved signaling information; and transmitting a broadcast signal including the modulated broadcast data and the modulated signaling information.

Methods, apparatus, and systems that relate to rate matching scheme design for polar coding, PAC coding, or other pre-transformed polar coding are described. One example method includes determining, by a first node, an output bit sequence having E bits based on an input bit sequence having K bits, wherein the output bit sequence is determined by 1) performing a polar transform with H components and 2) performing either no pre-transform or at least two pre-transform operations; wherein the polar transform is based on H polar matrices G.sup.(N.sup.0.sup.), G.sup.(N.sup.1.sup.), . . . , G.sup.(N.sup.H1.sup.), wherein H, K and E are integers greater than 1, wherein a polar matrix G.sup.(N.sup.i.sup.) is of size N.sub.i. The method also includes transmitting, by the first node, a signal including the output bit sequence to a second node.

Methods, apparatus, and systems that relate to rate matching scheme design for polar coding, PAC coding, or other pre-transformed polar coding are disclosed. In one example aspect, a method for digital communication includes determining, by a first node, an output bit sequence having E bits based on an input bit sequence having K bits, wherein the output bit sequence is determined by performing a polar transform with H components and a pre-transform; wherein the polar transform is based on H polar matrices G.sup.(N.sup.0.sup.), G.sup.(N.sup.1.sup.), . . . , G.sup.(N.sup.H0.sup.), wherein E, K, H are integers greater than 1, wherein a polar matrix G.sup.(N.sup.0.sup.) is of size N.sub.i. The method also includes transmitting, by the first node, a signal including the output bit sequence to a second node.

Methods, apparatus, and systems that relate to Polarization-Adjusted Convolutional (PAC) coding with variable lengths are disclosed. In one example aspect, a method for digital communication includes determining, by a first node, an output bit sequence having E bits based on an input bit sequence having K bits. The output bit sequence is determined based on a transform that is applied prior to applying a Polar transform having a size of N. The transform is based on at least one index set that is a subset of a set of bit indices. The set of bit indices comprises all non-negative integers that are less than N and wherein K<N and K<E. The method also includes transmitting, by the first node, a signal including the output bit sequence to a second node.

A memory system includes a controller and a semiconductor memory device. The semiconductor memory device stores a data set having main data bits and parity bits and provide soft decision bit streams corresponding to the data set in response to control signals of the controller. The controller includes a soft decision decoder for identifying data set by decoding the soft decision bit streams according to a first decoding method, a deinterleaver for deinterleaving the identified data set, a hard decision decoder for decoding the deinterleaved data set according to a second decoding method based on parity bits included in the deinterleaved data set, and outputting a failed data set if the decoding according to the second decoding method has failed, and an interleaver for interleaving the failed data set. The interleaved data set is fed back to the soft decision decoder.

Methods, apparatus, and systems that relate to rate matching scheme design for polar coding, PAC coding, or other pre-transformed polar coding are disclosed. In one example aspect, a method for digital communication includes determining, by a first node, an output bit sequence having E bits based on an input bit sequence c having K bits, wherein the output bit sequence is determined based on an output of a polar transform and an output of a repetition operation, and wherein the input of the repetition operation is a portion of a bit sequence before the polar transform. The method also includes transmitting, by the first node, a signal including the output bit sequence to a second node.

A DTV transmitting system includes a frame encoder, a randomizer, a block processor, a group formatter, a deinterleaver, and a packet formatter. The frame encoder builds an enhanced data frame and adds parity data into the data frame. The frame encoder further divides the data frame into first and second sub-frames including first and second portions of the parity data, respectively, and permutes a plurality of the first sub-frames and a plurality of the second sub-frames, respectively. The randomizer randomizes enhanced data in the permuted sub-frames, and the block processor codes the randomized data at a rate of 1/N1. The group formatter forms a group of enhanced data having one or more data regions and inserts the 1/N1 coded data into at least one of the data regions. The deinterleaver deinterleaves the group of enhanced data, and the packet formatter formats the deinterleaved data into enhanced data packets.

A codeword is generated based on a segmentation transform and a Polarization-Adjusted Convolutional (PAC) code that includes an outer convolutional code and a polar code, and based on separate encoding of respective different segments of convolutionally encoded input bits according to the polar code. Each segment of the respective segments includes multiple bits of the convolutionally encoded input bits for which the separate encoding of the segment is independent of the separate encoding of other segments. Separate decoding may be applied to segments of such a codeword to decode convolutionally encoded input bits corresponding to the separately encoded segments of the convolutionally encoded input bits.

Devices, systems and methods for list decoding of polarization-adjusted convolutional (PAC) codes are described. One example method for improving error correction in a decoder for data in a communication channel includes receiving a noisy codeword, the codeword having been generated using a polarization-adjusted convolutional (PAC) code and provided to the communication channel prior to reception by the decoder, and performing PAC list decoding on the noisy codeword, wherein an encoding operation of the PAC code comprises a convolutional precoding operation that generates one or more dynamically frozen bits, and wherein the PAC list decoding comprises extending, based on the one or more dynamically frozen bits, at least two paths of a plurality of paths in the PAC list decoding differently and independently.