Coded Modulation An Information-Theoretic Perspective Young-Han Kim - - PowerPoint PPT Presentation

Coded Modulation An Information-Theoretic Perspective

Young-Han Kim http://young-han.kim Department of ECE UC San Diego Annual ACC Workshop Tel Aviv University January , 

Information theory of point-to-point communication

Channel

/

Information theory of point-to-point communication

M k ̂ M Pe Xn Yn Encoder p(y|x) Decoder

/

Information theory of point-to-point communication

M k ̂ M Pe Xn Yn Encoder p(y|x) Decoder

∙ “Baseband” picture of communication

/

Information theory of point-to-point communication

M k ̂ M Pe Xn Yn Encoder p(y|x) Decoder

∙ “Baseband” picture of communication ∙ Tradeoff between R = k/n, Pe = P(M ̸= ̂

M), and n

/

Information theory of point-to-point communication

M k ̂ M Pe Xn Yn Encoder p(y|x) Decoder

∙ “Baseband” picture of communication ∙ Tradeoff between R = k/n, Pe = P(M ̸= ̂

M), and n

∙ Capacity C: maximum R such that Pe →  as n → ∞

/

Information theory of point-to-point communication

M k ̂ M Pe Xn Yn Encoder p(y|x) Decoder

∙ “Baseband” picture of communication ∙ Tradeoff between R = k/n, Pe = P(M ̸= ̂

M), and n

∙ Capacity C: maximum R such that Pe →  as n → ∞

R C   Pe

/

Information theory of point-to-point communication

M k ̂ M Pe Xn Yn Encoder p(y|x) Decoder

∙ “Baseband” picture of communication ∙ Tradeoff between R = k/n, Pe = P(M ̸= ̂

M), and n

∙ Capacity C: maximum R such that Pe →  as n → ∞

R C   Pe

/

Information theory of point-to-point communication

M k ̂ M Pe Xn Yn Encoder p(y|x) Decoder

∙ “Baseband” picture of communication ∙ Tradeoff between R = k/n, Pe = P(M ̸= ̂

M), and n

∙ Capacity C: maximum R such that Pe →  as n → ∞

R C   Pe

/

Information theory of point-to-point communication

M k ̂ M Pe Xn Yn Encoder p(y|x) Decoder

∙ “Baseband” picture of communication ∙ Tradeoff between R = k/n, Pe = P(M ̸= ̂

M), and n

∙ Capacity C: maximum R such that Pe →  as n → ∞

/

Channel coding theorem (Shannon )

C = max

p(x) I(X; Y)

Gaussian channel

M k ̂ M Pe Xn Yn Encoder Decoder g Z

/

Gaussian channel

M k ̂ M Pe Xn Yn Encoder Decoder g Z

∙ Simple model for wireless, wired, and optical communication

/

Gaussian channel

M k ̂ M Pe Xn Yn Encoder Decoder g Z

∙ Simple model for wireless, wired, and optical communication ∙ Average power constraint ∑n

i= x i (m) ≤ nP

/

Gaussian channel

M k ̂ M Pe Xn Yn Encoder Decoder g Z

∙ Simple model for wireless, wired, and optical communication ∙ Average power constraint ∑n

i= x i (m) ≤ nP

∙ Channel quality measured by SNR = gP

/

Gaussian channel

M k ̂ M Pe Xn Yn Encoder Decoder g Z

∙ Simple model for wireless, wired, and optical communication ∙ Average power constraint ∑n

i= x i (m) ≤ nP

∙ Channel quality measured by SNR = gP Channel coding theorem (Shannon )

C = 

 log( + SNR)

/

Capacity of the Gaussian channel (Forney–Ungerboeck ’)

/

How to achieve the capacity?

∙ Random coding and joint typicality decoding

(Shannon , Forney , Cover )

/

How to achieve the capacity?

∙ Random coding and joint typicality decoding

(Shannon , Forney , Cover )

/

X n

How to achieve the capacity?

∙ Random coding and joint typicality decoding

(Shannon , Forney , Cover )

/

X n xn(m)

How to achieve the capacity?

∙ Random coding and joint typicality decoding

(Shannon , Forney , Cover )

∙ Find a unique m such that (xn(m), yn) is jointly typical w.r.t. p(x, y)

/

X n Yn yn xn(m)

How to achieve the capacity?

∙ Random coding and joint typicality decoding

(Shannon , Forney , Cover )

∙ Find a unique m such that (xn(m), yn) is jointly typical w.r.t. p(x, y) ∙ Successful w.h.p. if R < I(X; Y)

/

X n Yn yn xn(m)

The other half of the story

∙ Average performance of randomly generate codes is good

㶳 Probabilistic method: there exists a good code

/

The other half of the story

∙ Average performance of randomly generate codes is good

㶳 Probabilistic method: there exists a good code 㶳 Most codes are good

/

The other half of the story

∙ Average performance of randomly generate codes is good

㶳 Probabilistic method: there exists a good code 㶳 Most codes are good 㶳 Works for any alphabet

/

The other half of the story

∙ Average performance of randomly generate codes is good

㶳 Probabilistic method: there exists a good code 㶳 Most codes are good 㶳 Works for any alphabet 㶳 “All codes are good, except those that we know of”

(Wozencraft–Reiffen , Forney )

/

The other half of the story

∙ Average performance of randomly generate codes is good

㶳 Probabilistic method: there exists a good code 㶳 Most codes are good 㶳 Works for any alphabet 㶳 “All codes are good, except those that we know of”

(Wozencraft–Reiffen , Forney )

∙ Coding theory

㶳 Algebraic: Hamming, Reed–Solomon, BCH, Reed–Muller, polar codes 㶳 Probabilistic: LDPC, turbo, raptor, spatially coupled codes

/

The other half of the story

∙ Average performance of randomly generate codes is good

㶳 Probabilistic method: there exists a good code 㶳 Most codes are good 㶳 Works for any alphabet 㶳 “All codes are good, except those that we know of”

(Wozencraft–Reiffen , Forney )

∙ Coding theory

㶳 Algebraic: Hamming, Reed–Solomon, BCH, Reed–Muller, polar codes 㶳 Probabilistic: LDPC, turbo, raptor, spatially coupled codes

∙ Coding practice

㶳 G LTE: Turbo and convolutional codes 㶳 G NR: LDPC and polar codes

/

The other half of the story

∙ Average performance of randomly generate codes is good

㶳 Probabilistic method: there exists a good code 㶳 Most codes are good 㶳 Works for any alphabet 㶳 “All codes are good, except those that we know of”

(Wozencraft–Reiffen , Forney )

∙ Coding theory

㶳 Algebraic: Hamming, Reed–Solomon, BCH, Reed–Muller, polar codes 㶳 Probabilistic: LDPC, turbo, raptor, spatially coupled codes

∙ Coding practice

㶳 G LTE: Turbo and convolutional codes 㶳 G NR: LDPC and polar codes 㶳 Everything is binary

/

Coded modulation

M k CN Xn Encoder Coded modulation Binary ECC

∙ Communication rate: R = (code rate) × (modulation rate) = k

N ⋅ N n = k n

/

Coded modulation

M k CN Xn Encoder Coded modulation Binary ECC

∙ Communication rate: R = (code rate) × (modulation rate) = k

N ⋅ N n = k n

∙ BPSK: X = {−倂P, +倂P} and N = n

 㨃→ +倂P  㨃→ −倂P

/

Coded modulation

M k CN Xn Encoder Coded modulation Binary ECC

∙ Communication rate: R = (code rate) × (modulation rate) = k

N ⋅ N n = k n

∙ BPSK: X = {−倂P, +倂P} and N = n

 㨃→ +倂P  㨃→ −倂P

∙ Sometimes multiple, independent (binary) codewords are modulated together

/

Coded modulation

M k CN Xn Encoder Coded modulation Binary ECC

∙ Communication rate: R = (code rate) × (modulation rate) = k

N ⋅ N n = k n

∙ BPSK: X = {−倂P, +倂P} and N = n

 㨃→ +倂P  㨃→ −倂P

∙ Sometimes multiple, independent (binary) codewords are modulated together ∙ We decompose coded modulation into two operations

/

Coded modulation

M k CN Xn Encoder Coded modulation Binary ECC

∙ Communication rate: R = (code rate) × (modulation rate) = k

N ⋅ N n = k n

∙ BPSK: X = {−倂P, +倂P} and N = n

 㨃→ +倂P  㨃→ −倂P

∙ Sometimes multiple, independent (binary) codewords are modulated together ∙ We decompose coded modulation into two operations

㶳 Symbol-level mapping: X = ϕ(U, U, . . . , UL), Ul ∈ {±}

/

Coded modulation

M k CN Xn Encoder Coded modulation Binary ECC

∙ Communication rate: R = (code rate) × (modulation rate) = k

N ⋅ N n = k n

∙ BPSK: X = {−倂P, +倂P} and N = n

 㨃→ +倂P  㨃→ −倂P

∙ Sometimes multiple, independent (binary) codewords are modulated together ∙ We decompose coded modulation into two operations

㶳 Symbol-level mapping: X = ϕ(U, U, . . . , UL), Ul ∈ {±} 㶳 Block-level mapping: Un

l = ψ(CN), l = , . . . , L

/

Multiple layers and symbol-level mapping

        b b bb U U X

∙ Natural mapping: X = α(U + U)

/

Multiple layers and symbol-level mapping

      b b bb U U X   ϕ

∙ Natural mapping: X = α(U + U) ∙ Gray mapping: X = α(UU + U)

/

Multiple layers and symbol-level mapping

      b b bb U U X   ϕ

∙ Natural mapping: X = α(U + U) ∙ Gray mapping: X = α(UU + U) ∙ Similar mapping ϕ exists for higher-order PAM, QPSK, QAM, PSK, MIMO, ...

XQPSK = 倂P exp急i π(UU + U)  怵

/

Multiple layers and symbol-level mapping

      b b bb U U X   ϕ

∙ Natural mapping: X = α(U + U) ∙ Gray mapping: X = α(UU + U) ∙ Similar mapping ϕ exists for higher-order PAM, QPSK, QAM, PSK, MIMO, ...

XQPSK = 倂P exp急i π(UU + U)  怵

∙ Can be many-to-one (still information-lossless)

   

∙ Can induce nonuniform X (Gallager )

/

Horizontal superposition coding

M M Un



Un



Xn ϕ

/

Horizontal superposition coding

M M Un



Un



Xn ϕ

/

∙ Broadcast channels (Cover ), fading channels (Shamai–Steiner )

Horizontal superposition coding

M M Un



Un



Xn ϕ

/

∙ Broadcast channels (Cover ), fading channels (Shamai–Steiner ) ∙ Successive cancellation decoding:

Horizontal superposition coding

M M Un



Un



Xn ϕ

/

∙ Broadcast channels (Cover ), fading channels (Shamai–Steiner ) ∙ Successive cancellation decoding:

㶳 Find a unique m such that (un

(m), yn) is jointly typical: R < I(U; Y)

Horizontal superposition coding

M M Un



Un



Xn ϕ

/

∙ Broadcast channels (Cover ), fading channels (Shamai–Steiner ) ∙ Successive cancellation decoding:

㶳 Find a unique m such that (un

(m), yn) is jointly typical: R < I(U; Y)

㶳 Find a unique m such that (un

 (m), un (m), yn) is jointly typical: R < I(U; U, Y)

Horizontal superposition coding

M M Un



Un



Xn ϕ

/

∙ Broadcast channels (Cover ), fading channels (Shamai–Steiner ) ∙ Successive cancellation decoding:

㶳 Find a unique m such that (un

(m), yn) is jointly typical: R < I(U; Y)

㶳 Find a unique m such that (un

 (m), un (m), yn) is jointly typical: R < I(U; U, Y)

㶳 Combined rate:

R + R < I(U; Y, U) + I(U; Y)

Horizontal superposition coding

M M Un



Un



Xn ϕ

/

∙ Broadcast channels (Cover ), fading channels (Shamai–Steiner ) ∙ Successive cancellation decoding:

㶳 Find a unique m such that (un

(m), yn) is jointly typical: R < I(U; Y)

㶳 Find a unique m such that (un

 (m), un (m), yn) is jointly typical: R < I(U; U, Y)

㶳 Combined rate:

R + R < I(U; Y, U) + I(U; Y) = I(U, U; Y)

Horizontal superposition coding

M M Un



Un



Xn ϕ

/

∙ Broadcast channels (Cover ), fading channels (Shamai–Steiner ) ∙ Successive cancellation decoding:

㶳 Find a unique m such that (un

(m), yn) is jointly typical: R < I(U; Y)

㶳 Find a unique m such that (un

 (m), un (m), yn) is jointly typical: R < I(U; U, Y)

㶳 Combined rate:

R + R < I(U; Y, U) + I(U; Y) = I(U, U; Y) = I(X; Y)

Horizontal superposition coding

M M Un



Un



Xn ϕ

/

∙ Broadcast channels (Cover ), fading channels (Shamai–Steiner ) ∙ Successive cancellation decoding:

㶳 Find a unique m such that (un

(m), yn) is jointly typical: R < I(U; Y)

㶳 Find a unique m such that (un

 (m), un (m), yn) is jointly typical: R < I(U; U, Y)

㶳 Combined rate:

R + R < I(U; Y, U) + I(U; Y) = I(U, U; Y) = I(X; Y)

㶳 Regardless of ϕ or the decoding order

Horizontal superposition coding

M M Un



Un



Xn ϕ

/

∙ Broadcast channels (Cover ), fading channels (Shamai–Steiner ) ∙ Successive cancellation decoding:

㶳 Find a unique m such that (un

(m), yn) is jointly typical: R < I(U; Y)

㶳 Find a unique m such that (un

 (m), un (m), yn) is jointly typical: R < I(U; U, Y)

㶳 Combined rate:

R + R < I(U; Y, U) + I(U; Y) = I(U, U; Y) = I(X; Y)

㶳 Regardless of ϕ or the decoding order

∙ Multi-level coding (MLC): Wachsmann–Fischer–Huber ()

Vertical superposition coding

M Un



Un



Xn ϕ

/

Vertical superposition coding

M Un



Un



Xn ϕ

/

∙ Single codeword of length n: Cn = (Cn, Cn

n+)

Cn 㨃→ Un



Cn

n+ 㨃→ Un 

Vertical superposition coding

M Un



Un



Xn ϕ

/

∙ Single codeword of length n: Cn = (Cn, Cn

n+)

Cn 㨃→ Un



Cn

n+ 㨃→ Un 

∙ Treating the other layer as noise:

Vertical superposition coding

M Un



Un



Xn ϕ

/

∙ Single codeword of length n: Cn = (Cn, Cn

n+)

Cn 㨃→ Un



Cn

n+ 㨃→ Un 

∙ Treating the other layer as noise:

㶳 Find a unique m such that

(un

 (m), yn) is jointly typical

and (un

(m), yn) is jointly typical

Vertical superposition coding

M Un



Un



Xn ϕ

/

∙ Single codeword of length n: Cn = (Cn, Cn

n+)

Cn 㨃→ Un



Cn

n+ 㨃→ Un 

∙ Treating the other layer as noise:

㶳 Find a unique m such that

(un

 (m), yn) is jointly typical

and (un

(m), yn) is jointly typical

㶳 Successful w.h.p. if

R < I(U; Y) + I(U; Y)

Vertical superposition coding

M Un



Un



Xn ϕ

/

∙ Single codeword of length n: Cn = (Cn, Cn

n+)

Cn 㨃→ Un



Cn

n+ 㨃→ Un 

∙ Treating the other layer as noise:

㶳 Find a unique m such that

(un

 (m), yn) is jointly typical

and (un

(m), yn) is jointly typical

㶳 Successful w.h.p. if

R < I(U; Y) + I(U; Y) < I(U, U; Y) = I(X; Y)

Vertical superposition coding

M Un



Un



Xn ϕ

/

∙ Single codeword of length n: Cn = (Cn, Cn

n+)

Cn 㨃→ Un



Cn

n+ 㨃→ Un 

∙ Treating the other layer as noise:

㶳 Find a unique m such that

(un

 (m), yn) is jointly typical

and (un

(m), yn) is jointly typical

㶳 Successful w.h.p. if

R < I(U; Y) + I(U; Y) < I(U, U; Y) = I(X; Y)

∙ Bit-interleaved coded modulation (BICM): Caire–Taricco–Biglieri ()

Diagonal superposition coding

M Un



Un



Xn ϕ

/

Diagonal superposition coding

M㰀㰀 M㰀 Un



Un



Xn ϕ

/

Diagonal superposition coding

Un



Un



Xn ϕ M(j − ) M(j)

/

∙ Think outside the block: Sequence of messages M(j) mapped to Cn(j)

       U U Block

Diagonal superposition coding

Un



Un



Xn ϕ M(j − ) M(j)

/

∙ Think outside the block: Sequence of messages M(j) mapped to Cn(j)

       U U Block Cn

n+()

Cn()

Diagonal superposition coding

Un



Un



Xn ϕ M(j − ) M(j)

/

∙ Think outside the block: Sequence of messages M(j) mapped to Cn(j)

       U U Block Cn

n+()

Cn

n+()

Cn() Cn()

Diagonal superposition coding

Un



Un



Xn ϕ M(j − ) M(j)

/

∙ Think outside the block: Sequence of messages M(j) mapped to Cn(j)

       U U Block Cn

n+()

Cn

n+()

Cn

n+()

Cn() Cn() Cn()

Diagonal superposition coding

Un



Un



Xn ϕ M(j − ) M(j)

/

∙ Think outside the block: Sequence of messages M(j) mapped to Cn(j)

       U U Block Cn

n+()

Cn

n+()

Cn

n+()

Cn

n+()

Cn() Cn() Cn() Cn()

Diagonal superposition coding

Un



Un



Xn ϕ M(j − ) M(j)

/

∙ Think outside the block: Sequence of messages M(j) mapped to Cn(j)

       U U Block Cn

n+()

Cn

n+()

Cn

n+()

Cn

n+()

Cn

n+()

Cn() Cn() Cn() Cn() Cn()

Diagonal superposition coding

Un



Un



Xn ϕ M(j − ) M(j)

/

∙ Think outside the block: Sequence of messages M(j) mapped to Cn(j)

       U U Block Cn

n+()

Cn

n+()

Cn

n+()

Cn

n+()

Cn

n+()

Cn

n+()

Cn() Cn() Cn() Cn() Cn() Cn()

Diagonal superposition coding

Un



Un



Xn ϕ M(j − ) M(j)

/

∙ Think outside the block: Sequence of messages M(j) mapped to Cn(j)

       U U Block Cn

n+()

Cn

n+()

Cn

n+()

Cn

n+()

Cn

n+()

Cn

n+()

Cn() Cn() Cn() Cn() Cn() Cn()

∙ Sliding-window decoding:

Diagonal superposition coding

Un



Un



Xn ϕ M(j − ) M(j)

/

∙ Think outside the block: Sequence of messages M(j) mapped to Cn(j)

       U U Block Cn

n+()

Cn

n+()

Cn

n+()

Cn

n+()

Cn

n+()

Cn() Cn() Cn() Cn() Cn()

∙ Sliding-window decoding: R < I(U; U, Y) + I(U; Y) = I(X; Y)

Diagonal superposition coding

Un



Un



Xn ϕ M(j − ) M(j)

/

∙ Think outside the block: Sequence of messages M(j) mapped to Cn(j)

       U U Block Cn

n+()

Cn

n+()

Cn

n+()

Cn

n+()

Cn

n+()

Cn() Cn() Cn() Cn() Cn()

∙ Sliding-window decoding: R < I(U; U, Y) + I(U; Y) = I(X; Y) ∙ Block Markov coding: Used extensively in relay and feedback communication

Diagonal superposition coding

Un



Un



Xn ϕ M(j − ) M(j)

/

∙ Think outside the block: Sequence of messages M(j) mapped to Cn(j)

       U U Block Cn

n+()

Cn

n+()

Cn

n+()

Cn

n+()

Cn

n+()

Cn() Cn() Cn() Cn() Cn()

∙ Sliding-window decoding: R < I(U; U, Y) + I(U; Y) = I(X; Y) ∙ Block Markov coding: Used extensively in relay and feedback communication ∙ Sliding-window coded modulation (SWCM): Kim et al. (), Wang et al. ()

Multiple-antenna transmission

∙ Consider the signal layers U and U as antenna ports: X = (U, U)

/

Multiple-antenna transmission

∙ Consider the signal layers U and U as antenna ports: X = (U, U) ∙ Bell Laboratories Layered Space-Time (BLAST) architectures:

/

Multiple-antenna transmission

∙ Consider the signal layers U and U as antenna ports: X = (U, U) ∙ Bell Laboratories Layered Space-Time (BLAST) architectures:

㶳 Horizontal: H-BLAST (Foschini et al. /), also known as V-BLAST

/

Multiple-antenna transmission

∙ Consider the signal layers U and U as antenna ports: X = (U, U) ∙ Bell Laboratories Layered Space-Time (BLAST) architectures:

㶳 Horizontal: H-BLAST (Foschini et al. /), also known as V-BLAST 㶳 Diagonal: D-BLAST (Foschini )

/

Multiple-antenna transmission

∙ Consider the signal layers U and U as antenna ports: X = (U, U) ∙ Bell Laboratories Layered Space-Time (BLAST) architectures:

㶳 Horizontal: H-BLAST (Foschini et al. /), also known as V-BLAST 㶳 Diagonal: D-BLAST (Foschini ) 㶳 Vertical: Single-outer code (Foschini et al. ), but shouldn’t this be “V-BLAST”?

/

Multiple-antenna transmission

∙ Consider the signal layers U and U as antenna ports: X = (U, U) ∙ Bell Laboratories Layered Space-Time (BLAST) architectures:

㶳 Horizontal: H-BLAST (Foschini et al. /), also known as V-BLAST 㶳 Diagonal: D-BLAST (Foschini ) 㶳 Vertical: Single-outer code (Foschini et al. ), but shouldn’t this be “V-BLAST”?

∙ Signal layers can be far more general than antenna ports

/

Multiple-antenna transmission

∙ Consider the signal layers U and U as antenna ports: X = (U, U) ∙ Bell Laboratories Layered Space-Time (BLAST) architectures:

㶳 Horizontal: H-BLAST (Foschini et al. /), also known as V-BLAST 㶳 Diagonal: D-BLAST (Foschini ) 㶳 Vertical: Single-outer code (Foschini et al. ), but shouldn’t this be “V-BLAST”?

∙ Signal layers can be far more general than antenna ports ∙ Coded modulation can encompass MIMO transmission

U U U U

/

Comparison

/

Comparison

Horizontal

U U M M

Multi-level coding (MLC) R < I(U; Y) R < I(U; U, Y) Short, nonuniversal

/

Comparison

Horizontal

U U M M

Multi-level coding (MLC) R < I(U; Y) R < I(U; U, Y) Short, nonuniversal Vertical

M M

Bit-interleaved coded modulation (BICM) R < I(U; Y) + I(U; Y) Other layers as noise

/

Comparison

Horizontal

U U M M

Multi-level coding (MLC) R < I(U; Y) R < I(U; U, Y) Short, nonuniversal Vertical

M M

Bit-interleaved coded modulation (BICM) R < I(U; Y) + I(U; Y) Other layers as noise Diagonal

M M

Sliding-window coded modulation (SWCM) R < I(U; U, Y) + I(U; Y) = I(X; Y) Error prop., rate loss

/

BICM vs. SWCM

5 10 15 20 25 30 0.5 1 1.5 2 2.5 3 3.5 4

4PAM 8PAM 16PAM

SNR(dB) Symmetric Rate SWCM BICM

LTE turbo code / ≤-iteration LOG-MAP decoding at b = , n = , BLER = .

/

BICM vs. SWCM

5 10 15 20 25 30 0.5 1 1.5 2 2.5 3 3.5 4

4PAM 8PAM 16PAM

SNR(dB) Symmetric Rate SWCM BICM

LTE turbo code / ≤-iteration LOG-MAP decoding at b = , n = , BLER = .

/

Application: Interference channels

desired signal interference

/

Optimal rate region (Bandemer–El-Gamal–Kim )

X X Y Y p(y|x, x) p(y|x, x)

/

Optimal rate region (Bandemer–El-Gamal–Kim )

X X Y Y p(y|x, x) p(y|x, x)

/

R < I(X; Y|X) R + R < I(X, X; Y)

• r

R < I(X; Y)

R R

Optimal rate region (Bandemer–El-Gamal–Kim )

X X Y Y p(y|x, x) p(y|x, x)

/

R < I(X; Y|X) R + R < I(X, X; Y)

• r

R < I(X; Y)

R R

Optimal rate region (Bandemer–El-Gamal–Kim )

X X Y Y p(y|x, x) p(y|x, x)

/

R < I(X; Y|X) R + R < I(X, X; Y)

• r

R < I(X; Y)

R R

Low-complexity (implementable) alternatives

/

X X Y Y p(y|x, x) p(y|x, x) R R

Low-complexity (implementable) alternatives

∙ PP decoding

/

X X Y Y p(y|x, x) p(y|x, x) R R

Low-complexity (implementable) alternatives

∙ PP decoding

㶳 Treating interference as (Gaussian) noise: R < I(X; Y)

/

X X Y Y p(y|x, x) p(y|x, x) R R

Low-complexity (implementable) alternatives

∙ PP decoding

㶳 Treating interference as (Gaussian) noise: R < I(X; Y) 㶳 Successive cancellation decoding: R < I(X; Y), R < I(X; Y|X)

/

X X Y Y p(y|x, x) p(y|x, x) R R

Low-complexity (implementable) alternatives

∙ PP decoding

㶳 Treating interference as (Gaussian) noise: R < I(X; Y) 㶳 Successive cancellation decoding: R < I(X; Y), R < I(X; Y|X)

∙ + rate splitting (Zhao et al. , Wang et al. )

/

U U X X Y Y p(y|x, x) p(y|x, x) R R

Low-complexity (implementable) alternatives

∙ PP decoding

㶳 Treating interference as (Gaussian) noise: R < I(X; Y) 㶳 Successive cancellation decoding: R < I(X; Y), R < I(X; Y|X)

∙ + rate splitting (Zhao et al. , Wang et al. ) ∙ Novel codes

㶳 Spatially coupled codes (Yedla, Nguyen, Pfister, and Narayanan ) 㶳 Polar codes (Wang and S

¸as ¸o˘ glu )

/

X X Y Y p(y|x, x) p(y|x, x) R R

Sliding-window superposition coding (Wang et al. )

/

M(j − ) M(j) M(j) Un



Un



Xn



Xn



Yn



Yn



M(j) → M(j) M(j) → M(j) p(y|x, x) p(y|x, x)

Sliding-window superposition coding (Wang et al. )

/

M(j − ) M(j) M(j) Un



Un



Xn



Xn



Yn



Yn



M(j) → M(j) M(j) → M(j) p(y|x, x) p(y|x, x)        X U U Block M() M() M() M() M() M() M()

Sliding-window superposition coding (Wang et al. )

/

M(j − ) M(j) M(j) Un



Un



Xn



Xn



Yn



Yn



M(j) → M(j) M(j) → M(j) p(y|x, x) p(y|x, x)        X U U Block M() M() M() M() M() M() M() M() M()

Sliding-window superposition coding (Wang et al. )

/

M(j − ) M(j) M(j) Un



Un



Xn



Xn



Yn



Yn



M(j) → M(j) M(j) → M(j) p(y|x, x) p(y|x, x)        X U U Block M() M() M() M() M() M() M() M() M() M() M()

Sliding-window superposition coding (Wang et al. )

/

M(j − ) M(j) M(j) Un



Un



Xn



Xn



Yn



Yn



M(j) → M(j) M(j) → M(j) p(y|x, x) p(y|x, x)        X U U Block M() M() M() M() M() M() M() M() M() M() M() M() M()

Sliding-window superposition coding (Wang et al. )

/

M(j − ) M(j) M(j) Un



Un



Xn



Xn



Yn



Yn



M(j) → M(j) M(j) → M(j) p(y|x, x) p(y|x, x)        X U U Block M() M() M() M() M() M() M() M() M() M() M() M() M() M() M()

Sliding-window superposition coding (Wang et al. )

/

M(j − ) M(j) M(j) Un



Un



Xn



Xn



Yn



Yn



M(j) → M(j) M(j) → M(j) p(y|x, x) p(y|x, x)        X U U Block M() M() M() M() M() M() M() M() M() M() M() M() M() M() M() M() M()

Sliding-window superposition coding (Wang et al. )

/

M(j − ) M(j) M(j) Un



Un



Xn



Xn



Yn



Yn



M(j) → M(j) M(j) → M(j) p(y|x, x) p(y|x, x)        X U U Block M() M() M() M() M() M() M() M() M() M() M() M() M() M() M() M() M() M() M()

Sliding-window superposition coding (Wang et al. )

∙ Sliding-window coded modulation for sender  (without alphabet constraints)

/

M(j − ) M(j) M(j) Un



Un



Xn



Xn



Yn



Yn



M(j) → M(j) M(j) → M(j) p(y|x, x) p(y|x, x)        X U U Block M() M() M() M() M() M() M() M() M() M() M() M() M() M() M() M() M() M() M()

Sliding-window superposition coding (Wang et al. )

∙ Sliding-window decoding

/

M(j − ) M(j) M(j) Un



Un



Xn



Xn



Yn



Yn



M(j) → M(j) M(j) → M(j) p(y|x, x) p(y|x, x)        X U U Block M() M() M() M() M() M() M() M() M() M() M() M() M() M() M() M() M() M() M()

Sliding-window superposition coding (Wang et al. )

∙ Sliding-window decoding ∙ Successive cancellation decoding

/

M(j − ) M(j) M(j) Un



Un



Xn



Xn



Yn



Yn



M(j) → M(j) M(j) → M(j) p(y|x, x) p(y|x, x)        X U U Block M() M() M() M() M() M() M() M() M() M() M() M() M() M() M() M()

Sliding-window superposition coding (Wang et al. )

∙ Sliding-window decoding ∙ Successive cancellation decoding

R < I(X; Yj|U)

/

M(j − ) M(j) M(j) Un



Un



Xn



Xn



Yn



Yn



M(j) → M(j) M(j) → M(j) p(y|x, x) p(y|x, x)        X U U Block M() M() M() M() M() M() M() M() M() M() M() M() M()

Sliding-window superposition coding (Wang et al. )

∙ Sliding-window decoding ∙ Successive cancellation decoding

R < I(X; Yj|U) R < I(U; Yj) + I(U; Yj|U, X)

/

M(j − ) M(j) M(j) Un



Un



Xn



Xn



Yn



Yn



M(j) → M(j) M(j) → M(j) p(y|x, x) p(y|x, x)        X U U Block M() M() M() M() M() M() M() M() M() M() M() M()

Sliding-window superposition coding (Wang et al. )

∙ Every corner point: different decoding orders

/

M(j − ) M(j) M(j) Un



Un



Xn



Xn



Yn



Yn



M(j) → M(j) M(j) → M(j) p(y|x, x) p(y|x, x)        X U U Block M() M() M() M() M() M() M() M() M() M() M() M() M() M() M() M() M() M() M() R R

Sliding-window superposition coding (Wang et al. )

∙ Every corner point: different decoding orders ∙ Every point: time sharing or more superposition layers

/

M(j − ) M(j) M(j) Un



Un



Xn



Xn



Yn



Yn



M(j) → M(j) M(j) → M(j) p(y|x, x) p(y|x, x)        X U U Block M() M() M() M() M() M() M() M() M() M() M() M() M() M() M() M() M() M() M() R R

Sliding-window superposition coding (Wang et al. )

∙ Every corner point: different decoding orders ∙ Every point: time sharing or more superposition layers ∙ Extension to Han–Kobayashi (Wang et al. )

/

M(j − ) M(j) M(j) Un



Un



Xn



Xn



Yn



Yn



M(j) → M(j) M(j) → M(j) p(y|x, x) p(y|x, x)        X U U Block M() M() M() M() M() M() M() M() M() M() M() M() M() M() M() M() M() M() M() R R

Gaussian channel performance (Park–Kim–Wang )

8 9 10 11 12 INR (dB) 0.2 0.4 0.6 0.8 1 1.2 Symmetric Rate MLD SWCM SWCM (turbo) IAN IAN (turbo) 96% gain 154% gain 25% gain

LTE turbo code with b = , n = , BLER = ., SNR =  dB

/

System-level performance (Kim et al. )

/

Cooper’s Law

Source: Arraycomm, Zander–M¨ ah¨

• nen ()

/

Cooper’s Law

Source: Arraycomm, Zander–M¨ ah¨

• nen ()

∙ Gain over the past  years =  ∝ ηWsysNBS

/

Cooper’s Law

Source: Arraycomm, Zander–M¨ ah¨

• nen ()

∙ Gain over the past  years =  ∝ ηWsysNBS

㶳 Spectral efficiency η: x 

/

Cooper’s Law

Source: Arraycomm, Zander–M¨ ah¨

• nen ()

∙ Gain over the past  years =  ∝ ηWsysNBS

㶳 Spectral efficiency η: x  㶳 System bandwidth Wsys: x 

/

Cooper’s Law

Source: Arraycomm, Zander–M¨ ah¨

• nen ()

∙ Gain over the past  years =  ∝ ηWsysNBS

㶳 Spectral efficiency η: x  㶳 System bandwidth Wsys: x  㶳  of base stations NBS: x  (spatial reuse of frequency)

/

Concluding remarks

∙ Coded modulation as superposition coding

/

Concluding remarks

∙ Coded modulation as superposition coding

㶳 Simple and unifying picture

/

Concluding remarks

∙ Coded modulation as superposition coding

㶳 Simple and unifying picture 㶳 Framework for new coded modulation schemes

/

Concluding remarks

∙ Coded modulation as superposition coding

㶳 Simple and unifying picture 㶳 Framework for new coded modulation schemes

∙ Open problems

㶳 Finer analysis: Single-shot method (Verd´

u )

/

Concluding remarks

∙ Coded modulation as superposition coding

㶳 Simple and unifying picture 㶳 Framework for new coded modulation schemes

∙ Open problems

㶳 Finer analysis: Single-shot method (Verd´

u )

㶳 Shaping and dependence (a la Marton): CCDM (B¨

• cherer et al. )

/

Concluding remarks

∙ Coded modulation as superposition coding

㶳 Simple and unifying picture 㶳 Framework for new coded modulation schemes

∙ Open problems

㶳 Finer analysis: Single-shot method (Verd´

u )

㶳 Shaping and dependence (a la Marton): CCDM (B¨

• cherer et al. )

∙ To learn more

㶳 Kramer and Kim (), “Network information theory for cellular wireless,” in Information

Theoretic Perspectives on G Systems and Beyond, eds. Shamai, Simeone, and Maric

㶳 Wang et al. (), “Sliding-window superposition coding: Two-user interference

channels,” arXiv:.

㶳 Kim et al. (), “Interference management via sliding-window coded modulation for

G cellular networks,” IEEE Commun. Mag.

/