Various embodiments include an error correction code (ECC) system that provides protection against various errors in addition to data bit errors. In general, ECC codes protect against data bit errors, where one or more data bits in a data word contain the wrong value. The ECC code is based on the original data bits, such that a data bit error results in a data word that is inconsistent with the ECC code generated for and stored with the data word. The present embodiments generate ECC codes based on address information and/or sequencing information in addition to the data bits in the data word. As a result, the present embodiments detect bit errors in this address information and/or sequencing information. Such errors include write address decoding errors, read address decoding errors, write enable errors, and stale data errors.

An encoding circuit includes: a polar encoding unit capable of encoding a polar code of N bits; a frozen bit adding unit that generates a first sequence by adding frozen bits to an input signal; and a bit arrangement changing unit that: generates a second sequence of N bits by arranging the first sequence in the second sequence according to an arrangement rule dependent on a ratio of N.sub.t bits, being a code length of a polar code to be encoded and being N bits or less, and N bits, and setting bit values at bit positions other than positions where the first sequence is arranged in the second sequence to zero when N.sub.t bits are less than N bits; and inputs the second sequence to the polar encoding unit. A code word of N.sub.t bits is generated by thinning processing based on a result of encoding the second sequence.

A transmitter is provided. The transmitter includes: an outer encoder configured to encode input bits to generate outer-encoded bits including the input bits and parity bits; a zero padder configured to constitute Low Density Parity Check (LDPC) information bits including the outer-encoded bits and zero bits; and an LDPC encoder configured to encode the LDPC information bits, wherein the LDPC information bits are divided into a plurality of bit groups, and wherein the zero padder pads zero bits to at least some of the plurality of bit groups, each of which is formed of a same number of bits, to constitute the LDPC information bits based on a predetermined shortening pattern which provides that the some of the plurality of bit groups are not sequentially disposed in the LDPC information bits.

A transmitter is provided. The transmitter includes: an outer encoder configured to encode input bits to generate outer-encoded bits including the input bits and parity bits; a zero padder configured to generate a plurality of bit groups each of which is formed of a same number of bits, maps the outer-encoded bits to some of the bits in the bit groups, and pads zero bits to remaining bits in the bit groups, based on a predetermined shortening pattern, thereby to constitute Low Density Parity Check (LDPC) information bits; and an LDPC encoder configured to encode the LDPC information bits, wherein the remaining bits in which zero bits are padded include some of the bit groups which are not sequentially disposed in the LDPC information bits.

A transmitter is provided. The transmitter includes: a Low Density Parity Check (LDPC) encoder configured to encode input bits to generate parity bits; a parity permutator configured to perform parity permutation by interleaving the parity bits and group-wise interleaving a plurality of bit groups including the interleaved parity bits; and a puncturer configured to puncture some of the parity bits in the group-wise interleaved bit groups, wherein the parity permutator group-wise interleaves the bit groups such that some of the bit groups are positioned at predetermined positions, respectively, and a remainder of the bit groups are positioned without an order within the group-wise interleaved bit groups.

Method for sending first data as quantum information in qubits (Iφ>) and classical second data (S.sub.i) over a quantum channel (12; 12a; 12b), in particular in quantum information communication systems (10; 10a; 10b), which includes applying QECC encoding (111) to said qubits ((Iφ>) obtaining quantum information codewords (Iψ>), wherein said method (200; 300) includes applying (210) intentional errors (P.sub.i) with error syndromes (S.sub.i) representing said second classical data to said quantum information code-words ((Iψ>) obtaining quantum information codewords with intentional errors (P.sub.1) applied upon (P.sub.iIψ.sub.i>), and transmitting (220) from a transmitting side (11; 11a; 11b) said quantum information codewords with intentional errors applied upon (P.sub.iIψ.sub.i>) over said quantum channel (12; 12a) which outputs received codewords (P.sub.iIψ.sub.i>;E.sub.iP.sub.iIψ.sub.i>) at a receiving side (13; 13b), computing (230; 330) error syndromes (S.sub.i,R.sub.i) from said received codewords (P.sub.iIψ.sub.i>;E.sub.iP.sub.iIψ.sub.i>), performing a QECC error correction operation (250; 350) on said received codewords (P.sub.iIψ.sub.i>;E.sub.iP.sub.iIψ.sub.i>) by applying a correction operator (P.sub.i.sup.+; P.sub.i.sup.+E.sub.i.sup.+) obtained at least by said computed syndromes (S.sub.i; R.sub.i) to obtain corrected codewords (Iψ.sub.i>), outputting (260; 360) said corrected codewords (Iψ.sub.i>) and said computed syndromes (S.sub.i).

Disclosed in an embodiment of the present invention are a polar code encoding method and device, the method comprising: utilizing a common information bit set to represent each of m polar code blocks, the polar codes in each polar code block having the same code length and different code rates, and m being greater than or equal to 2; according to the common information bit set corresponding to the polar code block, acquiring an information bit set corresponding to each polar code in the polar code block; and according to the information bit set corresponding to each polar code in the polar code block, conducting polar code encoding on information to be encoded, thus reducing polar code representation overhead, and solving the problem in the prior art of excessively high polar code representation overhead.

A method of reading from a storage medium to recover a group of information sectors, each comprising a respective information payload. The medium stores redundancy data comprising a plurality of separate redundancy codes for the group, each code being a linear sum of terms, each term in the sum being the information payload from a different respective one of the information sectors in the group weighted by a respective coefficient of a set of coefficients for the redundancy code. The method comprises, after the redundancy data has already been stored on the medium: identifying a set of k′ information sectors to be recovered; selecting k′ of the redundancy codes; determining a square matrix E of the k′ information sectors by the k′ sets of coefficients of the selected codes; determining a matrix D being a matrix inverse of E; and recovering the k′ information payloads from the inverse matrix D.

The technology relates to an encoding device, an encoding method, a decoding device, a decoding method, and a program enabling encoding with favorable transmission efficiency with a controlled running disparity.

A calculation section divides inputted data into N or M bits to calculate a first running disparity of an N or M bit data string. A determination section determines whether the data string is inverted based on the first running disparity calculated by the calculation section and a second running disparity calculated therebefore. An addition section inverts or non-inverts the data string based on a determination result by the determination section to add a flag indicating the determination result for outputting. The determination section determines not to perform inversion when the data string is a control code. The addition section adds the flag assigned to the control code. The technology is applicable to a device communicating in an SLVS-EC specification.

Embodiment techniques map parity bits to sub-channels based on their row weights. In one example, an embodiment technique includes polar encoding, with an encoder of the device, information bits and at least one parity bit using the polar code to obtain encoded data, and transmitting the encoded data to another device. The polar code comprises a plurality of sub-channels. The at least one parity bit being placed in at least one of the plurality of sub-channels. The at least one sub-channel is selected from the plurality of sub-channels based on a weight parameter.